ABSTRACT

Title of Dissertation: JOSEPHSON EFFECTS IN THE
IRON-BASED SUPERCONDUCTOR FETE1−XSEX

Samuel Deitemyer
Doctor of Philosophy, 2025

Dissertation Directed by: Professor Steve Rolston
Department of Physics

Professor Steven M. Anlage
Department of Physics

The iron-based superconductor FeTe1−xSex has emerged as a promising platform for

combining superconductivity and topology in a single system, for the realization of topolog-

ical quantum computing. Besides this, FeTe1−xSex hosts rich physical phenomena such as

S± superconductivity, Majorana bound states, and higher-order topological superconduc-

tivity, among others. Despite the interest in superconducting devices based on FeTe1−xSex,

there have been relatively few demonstrations of Josephson junctions in FeTe1−xSex-based

systems.

In this dissertation we measured Josephson effects in a FeTe1−xSex-based device and

found three signatures of unconventional Josephson junction behavior. This first signature

was the existence of two distinct Josephson diffraction patterns under applied RF irradi-

ation, which likely arises from flux flow and a phase slip line in FeTe1−xSex. The second



signature was the emergence of sudden jumps in the DC current at which Shapiro steps

arise, as a function of applied RF power. This was measured by mapping dV
dI

vs DC current

and RF power. We provide two potential explanations for this phenomenon based on non-

equilibrium superconductivity. The third signature is a minimum critical current at zero

magnetic field when RF irradiation is present which resembles the π-Josephson junctions

formed as a consequence of multiband superconductivity.



JOSEPHSON EFFECTS IN THE IRON-BASED SUPERCONDUCTOR
FETE1−XSEX

by

Samuel Deitemyer

Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment

of the requirements for the degree of
Doctor of Philosophy

2025

Advisory Committee:

Professor Steve Rolston, Chair
Professor Steven M. Anlage, Chair
Professor Alicia J. Kollár
Professor Kasra Sardashti
Professor Christopher Jarzynski, Dean’s Representative



© Copyright by
Samuel Deitemyer

2025



Dedication

To my wife Tienne, your love and support truly made this possible. I couldn’t have done
it without your constant encouragement and positivity.

ii



Acknowledgements

I am deeply indebted to so many people who have helped me along the way out of the
goodness of their hearts.

Firstly, I would like to thank Professor Rolston and Professor Anlage for their support
and guidance throughout my graduation. I am sincerely grateful for all the effort and time
they have spent helping me.

I would also like to thank Professor Anlage for sharing his expertise in superconduc-
tivity inside and outside the classroom. Your interest in the topics always came through
and made learning fun.

I would like to thank Dr. Jimmy Williams for introducing me to research as an
undergraduate student and for mentoring me as a graduate student. I learned so much
from your mentorship, and for that, I am truly grateful.

I would like to extend my sincere thanks to Professor Kollár. You have been so
generous with your time, and I truly can not express how appreciative I am of your support
and kindness. On top of this, your coaching helped me land a job after graduation.

I would also like to thank Professor Cohen for his support and open-door policy.
Unfortunately, I abused that policy, but it was incredibly valuable to me to have chats
when I needed to.

I would like to thank Rodney Snyder for teaching me nearly everything I know about
measurements. You have been an excellent mentor and friend to so many.

I would also like to thank Professor Gong for supporting me during my time in his
group and for developing my written communication skills significantly.

There are so many others I want to thank, such as Doug Benson, John Abrahams,
Tom Loughran, Mark Lecates, Jon Hummel, Karen Gaskell, and many others, for their
technical support.

Additionally, I would like to thank all of my friends throughout my PhD who made
the experience enjoyable.

iii



Contents

Dedication ii

Acknowledgements iii

Table of Contents iv

List of Figures vi

1 Introduction 1
1.1 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Superconductivity 3
2.1 Introduction to Superconducting Phenomena . . . . . . . . . . . . . . . . . 3

3 Review of FeTeSe 9
3.1 Crystal Structure and Parent Compounds . . . . . . . . . . . . . . . . . . 9
3.2 Superconductivity in FeTeSe . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2.1 Notable Attempts to Increasing Tc . . . . . . . . . . . . . . . . . . 12
3.2.2 Fermi Surface/Pairing Mechanism/Pairing Symmetry . . . . . . . . 16

3.3 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3.1 Topology In FeTeSe . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4 Topological Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4.1 Topological Superconductivity in FeTeSe . . . . . . . . . . . . . . . 25
3.4.2 Higher Order Topological Superconductivity in FeTeSe . . . . . . . 28

3.5 Josephson Effects in FeTeSe-Based Devices . . . . . . . . . . . . . . . . . . 29

4 Josephson Junctions 32
4.1 Josephson Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1.1 Derivation of Josephson Equations . . . . . . . . . . . . . . . . . . 32
4.1.2 Shapiro Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1.3 Magnetic Field Dependence of Josephson Junctions . . . . . . . . . 39

5 FeTeSe-Al Josephson Junction 44
5.1 Fabrication and Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.1.1 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.1.2 Measurement Procedures . . . . . . . . . . . . . . . . . . . . . . . . 46

iv



5.2 Inner and outer junction effect . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2.1 Discussion of Inner/Outer Junction . . . . . . . . . . . . . . . . . . 57

5.3 Jumps in Shapiro Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3.1 Discussion of Jumps in Shapiro Mapping . . . . . . . . . . . . . . . 71

5.4 Magnetic Field dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.4.1 Fraunhofer Measurements of Inner Junction and the Outer Junction 76
5.4.2 Magnetic Field and RF Irradiation . . . . . . . . . . . . . . . . . . 78
5.4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6 Conclusion and Outlook 87

A Appendix 89
A.1 Lock-in, DC, RF, and B-Field in a Dilution Refrigerator . . . . . . . . . . 89

A.1.1 Lock-in Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 89
A.1.2 Current-Bias Measurements . . . . . . . . . . . . . . . . . . . . . . 90
A.1.3 Measurements in a dilution refrigerator . . . . . . . . . . . . . . . . 92
A.1.4 Magnetic Field and Superconducting Magnets . . . . . . . . . . . . 97

A.2 Failed Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
A.3 Wire Bonding Tips and Tricks . . . . . . . . . . . . . . . . . . . . . . . . . 99
A.4 Data dump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
A.5 Depositions System SOPs . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

References 139

v



List of Figures

2.1 Resistance vs Temperature curve for a superconductor. . . . . . . . . . . . 4
2.2 Diagram of the Meissner effect and the London penetration depth. . . . . 5
2.3 Diagram of relationship between critical temperature and critical field. . . 5
2.4 Diagram showing the critical current of a superconductor. . . . . . . . . . 6
2.5 Diagram showing the electron density of states around the Fermi energy in

a superconductor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.1 a,b) The 2D tetragonal crystal structure of FeTe1−xSex. The larger spacing
between layers bonded by weak vdW forces and smaller spacing in the layer
due to strong covalent bonds is visible in (a). The tetragonal structure is
most clear from the square structure visible along the c-axis of the material
(b). Adapted from Ref. [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Doping dependence of FeTe1−xSex, showing the antiferromagnetic state when
Se = 0.0 and the superconducting state from Se = 0.1 to Se = 1.0. The
references in the figure are; ‘Bulk-Ref [4]’: Ref. [15], ‘Bulk-Ref [11]’: Ref.
[16], ‘Crystal-Ref [3]’: Ref. [17]. Adapted from Ref. [18]. . . . . . . . . . 12

3.3 Resistance vs temperature that we measured for a FeTe0.55Se0.45 flake, show-
ing a Tc around 14 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.4 Tc enhancement by removing excess Fe atoms. The positions of excess Fe
atoms are shown to be at an interstitial location within the crystal. The
magnetic susceptibility and resistivity are shown as a function of temperature
for the higher Fe concentration (SC2, 11% excess Fe) and for the lower Fe
concentration (SC1, 3% excess Fe). The lower Fe concentration improves
the diamagnetic response and the Tc of the crystal. Adapted from Ref. [14]. 15

3.5 The effect of oxygen annealing on removing excess Fe and improving the
Tc. The diamagnetic response, critical temperature, and critical current are
all enhanced due to the effective removal of excess Fe by oxygen annealing.
Adapted from Ref. [19] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.6 A phase diagram showing the pressure and temperature-dependent behavior
of FeSe. Specifically, the pressure-dependent enhancement of Tc can be seen
until 10 GPa. Afterward, this FeSe begins to undergo a transition to the
hexagonal phase. Adapted from Ref. [23] . . . . . . . . . . . . . . . . . . 17

3.7 The calculated band structure (a) and Fermi surface (b) of LaFeAsO1−xFx.
The key properties here are two electron cylinders around the M point and
two hole cylinders around the Γ point. Adapted from Ref. [33] . . . . . . 18

vi



3.8 Quasiparticle interference probes of the unconventional superconductivity
of FeTeSe. a) The tunneling current as a function of position. b) The
tunneling current as a function of sample bias, showing the reduced tunneling
current due to the quasiparticle gap. c) The ratio of the conductance at
positive and negative voltage bias as a function of position. d) The Fourier
transform of (c) showing the quasiparticle intensity vs the wavevector. e)
The quasiparticle interference under a magnetic field of 10 T showing the
enhanced or suppressed scattering based on the phase difference between the
pockets, confirming the S± pairing symmetry. Adapted from Ref. [37] . . 19

3.9 Illustration of the band inversion effect giving rise to topological surface
states. The strong spin-orbit coupling opens a bandgap and causes twisting
of the bands (i.e., band inversion). At the interface with materials without
band inversion, the bands must be reverted to an untwisted non-inverted
state and must cross to do so. This closes the bandgap locally, giving rise to
topologically protected surface states. . . . . . . . . . . . . . . . . . . . . 21

3.10 First principles calculation of the band structure of FeTeSe, revealing band
inversion and a non-zero topological invariant. a) The band structure of
FeSe. b) the band structure of FeTeSe, neglecting the spin-orbit interaction.
The main difference from FeSe (a) is that the Γ2

− band (bolded in red) is
pushed down in energy and crosses the Fermi energy along the Γ-Z direction.
c) The band structure of FeTeSe after adding the spin-orbit interaction. d)
A zoom-in on the Γ-Z direction showing the avoided crossing which gives
rise to the band inversion and topology in FeTeSe. Adapted from Ref. [44] 23

3.11 Illustration of braiding operations on Majorana bound states. The Majorana
wavefunction starts in the ground states defined by pairs of Majorana par-
ticles. By exchanging the particles’ positions, the wavefunction will now be
in a superposition of the ground and excited states. For successive braiding
operations, the order of exchanges affects the final state. Adapted from Ref.
[43] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.12 Illustration of a vortex in a superconductor. The order parameter (ψ) is re-
duced inside a radius equal to the coherence length (ξ), eventually becoming
zero at the core of the vortex. The magnetic field intensity (H) decays over
the penetration depth of the superconductor (λ). . . . . . . . . . . . . . . 26

3.13 A direct probe of Majorana bound states at the core of a superconducting
vortex using STM. A peak in the conductance can be seen at the core of
the vortex using STM (a). This peak in the conductance can be shown
to be centered on zero energy, as well as at the core of the vortex (b).
An insensitivity to magnetic field was also demonstrated, ruling out CdGM
states and Kondo resonances (c,d). Adapted from Ref. [51] . . . . . . . . 27

3.14 Visualization of the S± superconductivity on the surfaces of FeTeSe, and the
resulting helical hinge zero modes. The closing of the superconducting gap
at an angle between the two surfaces of FeTeSe and the topological surface
states give rise to the higher order topology in this material. Adapted from
Ref. [58]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

vii



3.15 a-c) A transport study on FeTeSe (a) revealing a zero bias conductance peak
when the electrode is in contact with the edge of the sample (c), which is
absent when just contacting the top surface (b), confirming the presence of
helical hinge zero modes. The small peak in (b) is likely due to tunneling
through the hBN into the helical hinge zero mode, which exists at zero
energy. Adapted from Ref. [58]. . . . . . . . . . . . . . . . . . . . . . . . 29

3.16 a) A constriction Josephson junction fabricated from FeTeSe crystals. b)
Shapiro steps were reliable in this system, confirming the realization of a
Josephson junction in this device. Adapted from Ref. [59]. . . . . . . . . . 30

3.17 a) A FeTeSe-FeTeSe homojunction where the vdW gap between he crystals
allows for tunneling between the FeTeSe flakes. b) The complicated mag-
netic field dependence of the critical current, showing asymmetry in B and
a minimum close to zero. c) The description for the unusual magnetic field
dependence is a combination between 0-junction behavior (the typical case)
and π-junction behavior (arising in Josephson junctions with multiband su-
perconductors or magnetic insulating layers). Adapted from Ref. [61]. . . 31

4.1 Schematic of a Josephson junction showing the macroscopic wavefunction of
each superconducting electrode. . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 A typical current-voltage curve, where current is shown on the x-axis and
voltage is shown on the y-axis, adapted from Ref. [63]. . . . . . . . . . . . 36

4.3 Diagram of Shapiro step behavior of a Josephson junction. . . . . . . . . . 38
4.4 Diagram showing the magnetic field incident on a Josephson junction and

the closed loop utilized to determine the magnetic field dependence. . . . 40
4.5 Plot of the Fraunhofer pattern showing the normalized critical current as a

function of the magnetic flux. . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.1 a-f) Overview of the fabrication process of the Al-FeTeSe devices. First
exfoliation of the FeTeSe was performed (a), followed by spinning of an e-
beam resist (b). A device pattern was then written into the e-beam resist
and developed (c). Titanium/Aluminum 5 nm/50 nm was deposited by
magnetron sputtering (d), and the excess Al was removed during the liftoff
stage (e). This process was then repeated for Ti/Au 5 nm/ 50 nm, using
electron beam deposition instead of sputtering. . . . . . . . . . . . . . . . 45

5.2 Schematic and dimensions of FeTeSe device showing the side view and top
view. The FeTeSe flake is ∼1.8 µm wide and the Al electrode is ∼1.0 µm
wide. The intended device was at the Al-FeTeSe interface, which has an
area of 1.8 µm2, however we will see that other regions in the device can
potentially contribute as well. . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.3 Optical image of the FeTeSe device structure showing the electrodes used
for the four-terminal measurement. This four-terminal measurement should
isolate the voltage drop across the Al-FeTeSe interface, and a small amount
of the FeTeSe and Al materials as well, which we will see can potentially
have a significant impact. This measured region is circled in red. . . . . . 48

viii



5.4 Circuit schematic of the measurement technique used to investigate the de-
vice; the 4-terminal current-bias measurement with a DC voltage source and
an RF source. The lock in amplifier produced a low frequency AC voltage
excitation which we convert into a current excitation I+ using a bias resis-
tor. The lock-in then measures the differential resistance dV

dI
in Ohms using a

phase locked technique. This resistance was then measured as a function of
DC current using a voltage source and a bias resistor, and as a function of RF
frequency and power (using a SMB100A microwave signal generator). See
Appendix A.1.2 for a more detailed discussion of the measurement methods. 49

5.5 a,b) Initial dV
dI

vs I measurements of the FeTeSe device. An initial jump
from a 0 Ω state to a 3 Ω resistance state occurs around 0.25 µA (a). Two
other distinct jumps in resistance can be seen at 6 µA and 13 µA. We will
later find Josephson effects emerginf for both the jump at 0.25 µA (the inner
junction) and at 6 µA (the outer junction). The resistance jump at 13 µA
likely corresponds to the bulk Al electrode, which will be shown later. . . 50

5.6 dV
dI

vs I measurements at a frequency of 0.5 GHz and a RF power of -54 dBm.
This RF power corresponds to the output of the RF generator, not the RF
power incident on the device. At this power, there are clear oscillations of the
differential resistance. The peaks correspond to the jump between Shapiro
steps and the minima correspond to the Shapiro step plateaus. . . . . . . 52

5.7 The result of numerically integrating Fig. 5.6 to reveal the voltage as a
function of current and the associated Shapiro steps. The voltage is shown
in units of the characteristic voltage step V = hf/2e, which for 0.5 GHz is
1.0 µV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.8 a,b) Map of dV
dI

vs I vs RF power, revealing the Bessel function-like depen-
dence of the Shapiro steps (a). See Refs. [68, 73] for more details on the
dependence of the Shapiro steps in the current-bias, which follow a Bessel
function-like oscillation. When the scale is modified, additional features are
also visible in the range of -35 dBm to -25 dBm (b), which resemble Shapiro
steps (in the outer junction), but are not clearly resolvable in this sweep. . 54

5.9 a,b) Map of dV
dI

vs I vs RF power at 3.97 GHz. The minimum in the dV
dI

is still clearly visible for the inner junction (a). However, when the scale
is adjusted, additional peaks are visible, which strongly resemble a Shapiro
step map for the outer junction (b). . . . . . . . . . . . . . . . . . . . . . 55

5.10 a) Linear cuts of the dV
dI

vs I vs RF power map at 3.97 GHz. b) The I-V curves
resulting from numerically integrating the linear cuts in (a). The Shapiro
step height can not be clearly resolved due to the finite slope where the
plateaus in voltage would normally be. This arises from the 3 Ω background
from the normal state resistance of the inner junction. . . . . . . . . . . . 57

5.11 a) Linear cuts of the dV
dI

vs I vs RF power map at 3.97 GHz minus the
3 Ω background from the normal state of the inner junction. b) The I-V
curves resulting from numerically integrating the linear cuts in (a), revealing
quantized Shapiro steps at the expected voltages of 8.2 µV . This suggests
there are indeed Josephson effects for both the inner junction and outer
junction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

ix



5.12 a) Schematic of vortex flux flow, whereby vortices and antivortices nucleate
at weak points in the superconductor, and flow perpendicular to the su-
percurrent by the Magnus effect. The vortex contains quasiparticles states,
which, when moved, will result in finite dissipation and therefore a finite re-
sistance/voltage across the device. b) Schematic of a phase slip line, whereby
the vortices moving in the wake of the following vortex become sufficiently
deformed such that they are described by a normal dissipating line through-
out the device. See Refs. [78, 79] for a discussion of phase slip lines and
Refs. [80–82] for a discussion of the kinematic vortices in phase slip lines. 60

5.13 Diagram showing the voltage vs current curves arising due to the successive
nucleation of phase slip lines, adapted from Ref. [87]. Specifically, when the
current is increased, additional phase slip lines are generated, which con-
tribute the same amount of resistance to the device. This would result in
steps in the resistance vs current curves, which can also be seen from the
steadily increasing slope observed in the voltage vs current curves corre-
sponding to jumps in the resistance by ∼ 0.25Ω. . . . . . . . . . . . . . . 62

5.14 dV
dI

vs I measurements at a frequency of 3.97 GHz at a power of -6 dBm
(a) and 0.5 GHz at an RF power of -50 dBm (b). The absence of a clear,
consistent step height in resistance suggests that the generation of additional
phase slip lines does not have to do with the jumps measured in dV

dI
. This

suggests that if the Josephson effects are indeed generated by phase slip lines,
then there is likely a single flux flow region or phase slip line as opposed to
the generation of multiple phase slip lines. . . . . . . . . . . . . . . . . . . 63

5.15 A dV
dI

vs I vs RF power map at 3.45 GHz. A discontinuous jump in the
mapping can be seen at ∼-4 dBm. This jump is most evident in the jump in
the envelope of the Shapiro steps, which represents the transition to the fully
normal state. Another unusual feature of this jump is that, despite the RF
power being increased (which would typically decrease the critical current
due to heating effects), the current defining the envelope of the Shapiro steps
is actually enhanced after increasing the RF power beyond this jump. . . 65

5.16 A fine resolution mapping of dV
dI

vs I at a frequency of 3.55 GHz. In or-
der to determine if the jump is an artifact of the measurement and simply
corresponds to a shift in the applied power, we can see if the pattern after
the jump can be mapped to a region before the jump. The jump does not
appear to be an artifact of the measurement, as the pattern after the jump
(highlighted in blue) does not align with the pattern before the jump (high-
lighted in white). The envelope of the Shapiro steps was used as a guide to
decide how much to shift the pattern down. . . . . . . . . . . . . . . . . . 66

5.17 a-d) dV
dI

vs I vs RF power mapping at a frequency of 3.55 GHz, repeated 4
times. This demonstrates that the jumps are a real, repeatable phenomenon
and not due to a random occurrence, such as someone bumping the system.
However, it should be noted that this does seem to be a dynamic effect,
because in (d) there are two additional jumps at -3 dBm and at -2 dBm not
seen in (a), (b), and (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

x



5.18 dV
dI

vs I vs RF power mapping at a frequency of 3.98 GHz. In this measure-
ment, there is minimal change in the envelope of the Shapiro steps; however,
there is a clear change in the behavior of the junction. Specifically, there is
a discontinuous jump in the peaks in dV

dI
as a function of current, and the

slope of these peaks vs RF power and DC current changes after the jump.
Most interesting is the fact that the jump happens over a range of powers as
opposed to at a specific power. This likely rules out frequency infidelity as
causing the jumps, as there is unlikely to be a shift in the frequency that oc-
curs differently for positive and negative DC currents, unless it is a physical
property of the Josephson junction. . . . . . . . . . . . . . . . . . . . . . 68

5.19 a,b) dV
dI

vs I vs RF power mapping at a frequency of 3.35 GHz (a) and 3.5
GHz (b). At these frequencies, a small dip can be seen in the differential
resistance, which occurs at progressively lower currents as the RF power is
increased. These lines seem to precipitate the occurrence of jumps, and in
the case of the 3.5 GHz mapping (b), a reemergence of the Shapiro steps
after they had nearly disappeared. These precipitating lines further support
that the jumps in the Shapiro mapping are a physical phenomenon within
the device and not an artifact of the measurement, as they link the lower
power behavior before the jump to the higher power behavior where the
jump takes place. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.20 dV
dI

vs I vs RF power mapping at a frequency of 5 GHz. The precipitating
lines are visible within this mapping, but do not intersect the envelope of
the Shapiro steps. Consequently, there is no jump in the behavior of the
Josephson junction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.21 The Wyatt-Dayem effect demonstrates the enhanced critical current in su-
perconducting strips of Tin under RF irradiation. Specifically, Wyatt mea-
sured the critical current as a function of RF power at a range of tempera-
tures, reprinted from Ref. [90]. They found that for small RF powers, there
was an enhancement of the critical current with RF irradiation, and that
at large RF powers, the critical current was reduced, which is the typical
behavior and is due to heating effects. . . . . . . . . . . . . . . . . . . . . 74

5.22 Diagram showing the potential regions giving rise to the Josephson effects in
this device. The supercurrent is perpendicular to the magnetic field for the
phase slip lines and parallel to the magnetic field for the Al-FeTeSe interface.
In order to see the Fraunhofer effects usually present in Josephson junctions,
the Magnetic field would need to be perpendicular to the supercurrent. . . 75

5.23 The initial sweep of dV
dI

vs I vs B up to a magnetic field of 200 mT. In this
sweep, only the outer junction critical current is visible, and it appears to
oscillate before dropping to zero. . . . . . . . . . . . . . . . . . . . . . . . 76

5.24 A finer sweep of dV
dI

vs I vs B up from 0 mT to 30 mT. In this sweep,
oscillations of the critical current are visible, which resemble the Fraunhofer
pattern typical of Josephson junctions. A Fraunhofer pattern is shown next
to the data for reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

xi



5.25 A fine sweep of dV
dI

vs I vs B from -2 mT to 2 mT showing the magnetic
field oscillations of the inner junction. Concurrent with the typical case of
Fraunhofer diffraction, there is a maximum of the critical current at B=0
and the critical current decays to zero at ∼ 2mT . . . . . . . . . . . . . . . 79

5.26 A fine sweep of dV
dI

vs I vs B from -2 mT to 2 mT, taken under 2 GHz RF
irradiation at a power of -45 dBm. Similar to the case of no RF irradiation,
the critical current decays over ∼ 2mT . This is also the case for the Shapiro
steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.27 a,b) A fine sweep of dV
dI

vs I vs B from -2 mT to 2 mT, taken under 3.95 GHz
RF irradiation at a power of -9.5 dBm. A minimum in the critical current
of the outer junction can be found at B=0 (a). This unusual phenomenon is
typically only found in Josephson junctions with magnetic tunnel barriers or
multiband superconductor Josephson junctions. In contrast, at the same RF
power and frequency, the inner junction retains the critical current maximum
at B=0. This maximum is visible for the critical current as well as for the
first Shapiro step of the inner junction. . . . . . . . . . . . . . . . . . . . 81

5.28 a) dV
dI

vs I measurements at a frequency of 3.98 GHz, highlighting the RF
powers where the subsequent magnetic fields will be performed. b) dV

dI
vs I

and B at a frequency of 3.98 GHz and a power of -3 dBm (before the jump).
Here, a minimum of the critical current is observed at B=0; however, the
envelope is relatively unmodified and retains a maximum at B=0. c) dV

dI
vs

I and B at a frequency of 3.98 GHz and a power of -1 dBm (after the jump).
Here, both the Shapiro steps and the envelope of the Shapiro steps display
a minimum at B=0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.29 Magnetic diffraction pattern for a π-Josephson junction formed at a YBCO
corner junction, as was investigated by Wollman et al. [97]. The unique
aspects of this junction are the anisotropic multiband superconductivity,
such that there will be a relative phase difference of π between the Josephson
junction on the different edges. The primary consequences are a minimum
of the critical current at B=0 and oscillations of the critical current over
2Φ0/Φ as opposed to Φ0/Φ for a typical junction. This could explain the
roughly doubled scale of the magnetic oscillations in our outer junction (5
mT) vs our inner junction (2 mT). . . . . . . . . . . . . . . . . . . . . . . 86

A.1 A typical current-voltage curve, where current is shown on the x-axis and
voltage is shown on the y-axis, adapted from Ref. [63]. . . . . . . . . . . . 91

A.2 Lock-in current-bias measurements utilizing a 1 MΩ resistor to set the cur-
rent bias from the Lock-in voltage, resulting in the measurement of dV

dI
. A

Lock-in frequency of ∼ 13 Hz is typically used. . . . . . . . . . . . . . . . 93
A.3 Shapiro Steps plotted as V vs I and I vs V, showing that the current bias

measurement (V vs I) results in a well defined single value function which is
more easily measurable experimentally. . . . . . . . . . . . . . . . . . . . 94

A.4 Lock-in current-bias measurements utilizing a 1 MΩ resistor to set the cur-
rent bias from the Lock-in voltage and the DC voltage source, resulting in
the measurement of dV

dI
as a function of the DC current. . . . . . . . . . . 94

xii



A.5 Lock-in current-bias measurements utilizing a 1 MΩ resistor to set the cur-
rent bias from the Lock-in voltage and the DC voltage source, resulting in
the measurement of dV

dI
as a function of the DC current. Low-pass-filters and

a sapphire board are used to thermalize the electrons. . . . . . . . . . . . 95
A.6 Lock-in and DC current-bias measurements with the addition of a RF mi-

crowave source, resulting in the measurement of dV
dI

as a function of the DC
current and RF irradiation (frequency and power). Low-pass-filters and a
sapphire board are used to thermalize the electrons in the DC lines. RF at-
tenuators are used to reduce the heating from the higher temperature plates
through the RF lines. A DC block is used to stop the DC signal from being
shunted to the attenuator grounds. . . . . . . . . . . . . . . . . . . . . . . 96

A.7 a) An attempted FeTeSe-Au-Al Josephson junction. b) An attempted FeTeSe-
Gr-Al Josephson junction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

A.8 a) An attempted FeTeSe-FeTeSe crossbar Josephson junction, which dis-
played no superconductivity in the top FeTeSe flake, potentially due to
strain. b) A FeTeSe flake suspended over a SiO2 trench, with the intent
of applying strain through electrostatic gating. c) The resulting data from
the strain device, showing no control effect at 1.7 K. If this experiment were
to be repeated, the strain control near Tc should be easier to prove as a proof
of concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

A.9 Wirebonder V-shaped path of the tip. . . . . . . . . . . . . . . . . . . . . . 101
A.10 Wirebonder metal stuck to the bond pads which can be used for subsequent

bonds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
A.11 A table of the parameters corresponding to the measurements displayed in

the Data Dump Section. All data is from the same device measured in the
main results section, and is taken over a current range of -6.6 µA to 6.6 µA. 103

A.12 dV
dI

vs I vs RF power at 100 MHz. . . . . . . . . . . . . . . . . . . . . . . . 104
A.13 dV

dI
vs I vs RF power at 200 MHz. . . . . . . . . . . . . . . . . . . . . . . . 104

A.14 dV
dI

vs I vs RF power at 350 MHz. . . . . . . . . . . . . . . . . . . . . . . . 105
A.15 dV

dI
vs I vs RF power at 400 MHz. . . . . . . . . . . . . . . . . . . . . . . . 105

A.16 dV
dI

vs I vs RF power at 700 MHz. . . . . . . . . . . . . . . . . . . . . . . . 106
A.17 dV

dI
vs I vs RF power at 800 MHz. . . . . . . . . . . . . . . . . . . . . . . . 106

A.18 dV
dI

vs I vs RF power at 900 MHz. . . . . . . . . . . . . . . . . . . . . . . . 107
A.19 dV

dI
vs I vs RF power at 1.2 GHz. . . . . . . . . . . . . . . . . . . . . . . . 107

A.20 dV
dI

vs I vs RF power at 2 GHz. . . . . . . . . . . . . . . . . . . . . . . . . 108
A.21 dV

dI
vs I vs RF power at 3 GHz. . . . . . . . . . . . . . . . . . . . . . . . . 108

A.22 dV
dI

vs I vs RF power at 3.25 GHz. . . . . . . . . . . . . . . . . . . . . . . . 109
A.23 dV

dI
vs I vs RF power at 3.45 GHz. . . . . . . . . . . . . . . . . . . . . . . . 109

A.24 dV
dI

vs I vs RF power at 3.5 GHz. In this map the jump shown in the main
text is missing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

A.25 dV
dI

vs I vs RF power at 3.7 GHz. . . . . . . . . . . . . . . . . . . . . . . . 110
A.26 dV

dI
vs I vs RF power at 3.8 GHz. . . . . . . . . . . . . . . . . . . . . . . . 111

A.27 dV
dI

vs I vs RF power at 3.9 GHz. . . . . . . . . . . . . . . . . . . . . . . . 111
A.28 dV

dI
vs I vs RF power at 3.95 GHz. . . . . . . . . . . . . . . . . . . . . . . . 112

A.29 dV
dI

vs I vs RF power at 4 GHz. . . . . . . . . . . . . . . . . . . . . . . . . 112

xiii



A.30 dV
dI

vs I vs RF power at 7 GHz. . . . . . . . . . . . . . . . . . . . . . . . . 113
A.31 dV

dI
vs I vs Magnetic Field at 500 MHz. . . . . . . . . . . . . . . . . . . . . 113

A.32 dV
dI

vs I vs Magnetic Field at 800 MHz. . . . . . . . . . . . . . . . . . . . . 114
A.33 dV

dI
vs I vs Magnetic Field at 3.55 GHz. . . . . . . . . . . . . . . . . . . . . 114

A.34 dV
dI

vs I vs RF power at 3.55 GHz and 2 mT. . . . . . . . . . . . . . . . . . 115
A.35 dV

dI
vs I vs RF power at 6 GHz. . . . . . . . . . . . . . . . . . . . . . . . . 115

xiv



Chapter 1

Introduction

1.1 Thesis Overview

In this thesis, I hope to give readers some familiarity with Josephson effects, highlight the

development and state of research into the unconventional superconductor FeTe1−xSex, and

discuss some of the unusual results we found when performing cryogenic measurements of

FeTe1−xSex.

In Chapter 2, I will give a very brief overview of the basic phenomena of Super-

conductivity to prepare unfamiliar readers for discussions of FeTe1−xSex and Josephson

junctions.

In Chapter 3, I will review the development and current state of research regarding

the unconventional superconductor FeTe1−xSex. This section may be of interest for those

concerned with Majorana fermions in FeTe1−xSex.

In Chapter 4, I will give a basic description of Josephson junctions and the related

phenomena. Specifically, I will describe the Josephson equations, the AC Josephson effects,

and the Fraunhofer pattern arising in the presence of a magnetic field.

In Chapter 5, I will discuss the main results of our study, the Josephson effects in

a FeTe1−xSex-Aluminum Josephson junction. I will discuss the presence of two Josephson

1



effects at different energy scales, discontinuous jumps in the AC Josephson diffraction

pattern as RF power is increased, and the unusual magnetic diffraction pattern arising

under RF irradiation.

In Chapter 6, I will conclude by summarizing our findings and discussing some of the

future avenues for research on the unconventional superconductor FeTe1−xSex.

The Appendix contains information I hope will be useful for readers interested in

some specific details. This section covers the details of experimental methods, details of the

deposition systems, various technical methods (tips and tricks), and finally, a data dump of

the remaining data measured in the FeTe1−xSex-Al Josephson junction, not already shown

in Chapter 5.

2



Chapter 2

Superconductivity

2.1 Introduction to Superconducting Phenomena

In the following, I will give a brief introduction to the relevant physical phenomena of

superconductors, which I learned from the excellent Introduction to Superconductivity by

Michael Tinkham (Ref. [1]), as have many before me. This phenomenological description

will serve as a basis for understanding superconducting phenomena in typical superconduct-

ing systems, as well as provide a basis for the unconventional superconductor FeTe1−xSex,

which we utilized in our study.

Superconductivity was first discovered by Kamerlingh Onnes in 1911 (Ref. [2]). This

discovery was made possible by Onnes’s successful liquefaction of helium in 1908, for which

he would later receive the Nobel Prize. The successful liquification of helium opened the

door for generations of low-temperature experiments. However, only 3 years later, in 1911,

Onnes was researching the resistance of metals as a function of temperature, when he dis-

covered that, in Mercury, below a temperature of ∼4.2 K, the electric resistance of Mercury

became negligible. A schematic representation is shown in Fig. 2.1. This is a hallmark

behavior of superconducting materials , and shortly thereafter led to demonstrations of

persistent dissipationless current flow in a superconducting ring.

3



Figure 2.1: Resistance vs Temperature curve for a superconductor.

Another early phenomenon discovered in superconducting materials was the Meissner

effect, discovered by Meissner and Ochsenfeld in 1933 (Ref. [3]). The Meissner effect

is the demonstration of perfect diamagnetism by superconducting materials. Therefore,

superconductors expel magnetic fields from their interior, as shown in Fig. 2.2. As noted by

Tinkham (Ref. [1]), this would seem to be described by the perfect screening of the magnetic

fields by dissipationless currents in the superconductor. However, according to Faraday’s

law, a perfect conductor would not require that the magnetic flux equal to zero, and would

instead require that the time rate of change of the magnetic flux equal to zero, dB
dt

= 0.

This would trap the magnetic flux when the material entered the superconducting state.

In 1935 the London brothers formulated two equations, dJ
dt

= ne2

m
E and ∇ × J = −ne2

m
B

which result in the exponential screening and expulsion of magnetic fields over a length

known as the London penetration depth λL =
√

m
µ0nse2

.

An extension of this phenomenon, which flows naturally from the idea that super-

conductors and magnetic fields are antagonistic to each other, is the idea of the critical

field of a superconductor. This is a field large enough that the free energy cost to expel

4



Figure 2.2: Diagram of the Meissner effect and the London penetration depth.

the field is greater than the free energy gained by forming the superconducting condensate,

and therefore, superconductivity is destroyed. The critical field follows from a maximum

value at zero temperature to zero field at the critical temperature of the superconductor,

see Fig. 2.3. This relation is approximately described by Bc = Bc(0)(1− (T/Tc)2).

Figure 2.3: Diagram of relationship between critical temperature and critical field.

5



A related phenomenon in superconductors is the critical current density. This is the

maximum current density that a superconductor can maintain before the superconductivity

breaks down and transitions to the normal state, see Fig. 2.4. This breakdown of the

superconductivity is a direct consequence of the critical field of the superconductor. As the

current flows through a superconducting material, there will be a ‘self-field’ generated at

the surface of the superconductor. If this surpasses the critical field of the superconductor,

superconductivity is destroyed. For the simple case of a cylindrical superconducting wire,

the relation Jc = Bc

µ2
0λ

can be derived. Where Jc is the critical current density in the

superconductor defined as the critical current per unit area. This relation is modified in

samples with different geometries or when one of the length scales of the superconductor

is smaller than the London penetration depth.

Figure 2.4: Diagram showing the critical current of a superconductor.

Lastly, I will briefly touch on the two fundamental theories that describe the behav-

ior of superconductors. In 1957, Bardeen, Cooper, and Schrieffer established a microscopic

theory to describe how, below the superconducting transition temperature, an attractive

6



electron-phonon interaction can cause pairs of electrons to condense into a bosonic quan-

tum state. It would later be found that other interactions can give rise to superconduc-

tivity besides electron-phonon coupling, in so-called unconventional superconductors. This

condensate consists of Cooper pairs and is separated from electronic states by the super-

conducting gap, 2∆. Above this gap is an enhanced quasiparticle density of states, which

was ‘pushed’ out of the superconducting gap, see Fig. 2.5. These peaks in the density of

states can be used to identify the superconducting gap in a multitude of measurements.

The BCS theory is particularly useful in its description of quasiparticles states. These Bo-

goliubov quasiparticles are unpaired superpositions of electron and hole states which exists

outside of the superconducting gap. The existence of quasiparticles in superconductors has

a number of significant impacts on devices, which we will discuss in Chapter 5.

Figure 2.5: Diagram showing the electron density of states around the Fermi energy in a
superconductor.

7



In order to describe the spatially-dependent phenomena in superconductors, the

Ginzburg-Landau theory was developed, which defines a macroscopic order parameter

based on the theory of second-order phase transitions. This order parameter turns out

to be the macroscopic wavefunction of the superconductor and is defined as ψ = ψ0e
iφ.

Where ψ0 =
√
ns, and ns is the Cooper pair density. φ is the macroscopic phase of the

superconductor which is crucial for understanding the dynamics of systems involving su-

perconductors, as we will discuss in Chapter 4. It was later shown by Gor’kov that this

theory could be derived from the BCS theory. The wavefunction of a macroscopic su-

perconductor represented by a single phase leads to a number of interesting phenomena,

such as flux quantization, Type II superconductors, superconducting vortices, and most

importantly for this study, the Josephson effect. The Josephson effect occurs when two

superconductors are separated by a non-superconducting layer that is sufficiently thin to

allow for phase-coherent transport. In these devices, the phase difference between the two

superconductors evolves according to the Josephson equations, which will be discussed in

detail in Chapter 4.1.

8



Chapter 3

Review of FeTeSe

FeTe1−xSex is a class of materials derived from the parent compounds FeTe and FeSe, which

demonstrates varying material properties based on the ratio of Te to Se. Under certain sub-

stitutional compositions, the class of FeTe1−xSex crystals demonstrate superconductivity

and topological surface states, which has motivated significant research efforts aimed at the

realization of Majorana fermions, since the discovery of superconductivity in FeTe1−xSex

in 2008 (Ref. [4]). This came less than 1 year after the discovery of the first iron-based

superconductor LaOFeAs (Ref. [5]), which shocked the scientific community because su-

perconductivity and magnetism are considered antagonistic electronic phases.

3.1 Crystal Structure and Parent Compounds

FeTeSe and its parent compounds FeSe and FeTe are two-dimensional van der Waals (vdW)

materials. This means that they are composed of atomically thin 2D layers of strongly co-

valently bonded atoms, which are weakly bonded by van der Waals forces to subsequent

layers, as shown in Fig. 3.1. The prototypical example of a 2D material is graphene.

In 2004, single-layer graphene was produced using scotch tape to separate an individual

atomic layer from a bulk piece of graphite (Ref. [6]), which is known as graphene (Gr).

This demonstration of a free-standing 2D material challenged previous assumptions based

9



on early works by Pierls in 1935 (Ref. [7]) and Landau in 1937 (Ref. [8]), which implied that

divergent out-of-plane fluctuations would cause 2D materials to be unstable. Furthermore,

in 1966 (Ref. [9]), works by Mermin-Wagner suggested that there could be no long-range

order in one-dimensional or two-dimensional systems due to the enhancement of long-range

fluctuations. It should be noted that Honenburg is sometimes credited alongside Mermin

and Wagner for his earlier unpublished proof, and Berezinskii is sometimes credited as

well for his independent proof. It is now widely accepted that Gr was realizable because

it is not a perfect 2D system in the way the theoretical treatments assumed; the finite

size of graphene monolayers and out-of-plane displacements (ripples) of the 2D structure

relax the strict requirements of these theoretical works. The discovery of two-dimensional

layers of graphene led to intense research over the past 20 years. Many interesting phenom-

ena have now been demonstrated in 2D materials, and most significantly for this study,

superconductivity.

Besides being a 2D material, the layers of FeTeSe form a tetragonal PbO-type struc-

ture at room temperature, as can be seen from the diagram of FeSe shown in Fig. 3.1,

where a square structure can be seen along the c-axis. The central Fe atoms in vdW layer

are bonded to Se atoms, alternating above or below the Fe plane. In FeTeSe crystals, a per-

centage of Se atoms will be substituted with Te atoms according to the overall composition.

At lower temperatures, certain compositions of FeTeSe crystals undergo a structural tran-

sition to the orthorhombic phase, breaking the C4 rotational symmetry and resulting in C2

rotational symmetry. This occurs at ∼90 K in FeSe crystals and is related to an electron-

nematic phase transition (Ref. [10]). In FeTe, which is not superconducting, there is no

electronic-nematic transition. Instead, there is a phase transition to an antiferromagnetic

phase below ∼70 K (Ref. [11]).

10



Figure 3.1: a,b) The 2D tetragonal crystal structure of FeTe1−xSex. The larger spacing
between layers bonded by weak vdW forces and smaller spacing in the layer due to strong
covalent bonds is visible in (a). The tetragonal structure is most clear from the square
structure visible along the c-axis of the material (b). Adapted from Ref. [4].

11



3.2 Superconductivity in FeTeSe

3.2.1 Notable Attempts to Increasing Tc

As can be seen in the phase diagrams of FeTe1−xSex, the parent compound FeSe is a

superconductor with a Tc of ∼9 K in bulk crystals (Refs. [4, 12, 13]) and FeTe is an antifer-

romagnet which demonstrates no superconductivity (Ref. [11]). FeTe1−xSex demonstrates

superconductivity within a range of x=0.1 to x=1, depending on the growth process. De-

spite the non-superconducting nature of FeTe, when FeSe is substituted with Te, the Tc can

be enhanced to 14 K. For our FeTe0.55Se0.45 crystals, we measured the Tc in the range of

13 K to 14 K, see Fig. 3.3, which is in the typical range for this composition. The highest

Tc is typically measured in samples of FeTe0.6Se0.4 which can reach ∼15 K (Ref. [14]).

Figure 3.2: Doping dependence of FeTe1−xSex, showing the antiferromagnetic state when
Se = 0.0 and the superconducting state from Se = 0.1 to Se = 1.0. The references in the
figure are; ‘Bulk-Ref [4]’: Ref. [15], ‘Bulk-Ref [11]’: Ref. [16], ‘Crystal-Ref [3]’: Ref. [17].
Adapted from Ref. [18].

As with all superconductors, there have been substantial efforts to study and increase

the Tc of the family of FeTeSe materials, with the idea of understanding high-temperature

12



Figure 3.3: Resistance vs temperature that we measured for a FeTe0.55Se0.45 flake, showing
a Tc around 14 K.

superconductivity or realizing room-temperature superconductivity. Below, I give a sum-

mary of the efforts to enhance superconductivity in the class of FeTeSe superconductors.

Initial improvements to the Tc were mostly realized by improving the composition

of the crystals. As was mentioned previously, excess iron helps stabilize the growth of

FeTeSe crystals (Ref. [19]); however, it is detrimental to the material performance. This

was demonstrated in Ref. [14], where they showed an enhancement of the Tc (measured

from the onset of superconductivity) from 11.6 K to 14.8 K by reducing the Fe content from

Fe1.11Te0.6Se0.4 to Fe1.04Te0.6Se0.4, as is shown in Fig. 3.4. Further, magnetic susceptibility

measurements showed a sharp transition to a diamagnetic state in Fe1.04Te0.6Se0.4 suggesting

bulk superconductivity, whereas Fe1.11Te0.6Se0.4 samples showed a broad transition which

13



would suggest a reduction in the superconducting volume fraction. They suggested that

these excess Fe atoms, which sit between the vdW layers of FeTeSe, are coupled to the Fe

in the vdW layers and may lead to the localization of the superconductivity. In order to

solve the issue of the beneficial role of excess Fe for growth and the detrimental effect on

superconductivity, a number of groups investigated oxygen annealing methods to remove

excess Fe after the growth of FeTeSe crystals (Refs. [19–22]). Specifically, it was shown

that the excess Fe could be reduced from 1.5% to 0.1% by annealing at 400◦ C at ∼1.5%

molar ratio of oxygen to Fe for more than 1 hour (Ref. [19]). The Tc and Jc (critical current

density) were enhanced as the O2 percentage was increased, until around 1.5% when the

Jc started to slightly decrease, as is shown in Fig. 3.5.

Another method of increasing the Tc in the family of FeTeSe crystals was pressure.

In studies on FeSe crystals, the Tc was enhanced to ∼37 K by the application of ∼7-9

GPa of hydrostatic pressure (Refs. [23, 24]). At higher pressures, the Tc decreases, and a

hexagonal structure arises (Fig. 3.6). The initial increase in Tc up to ∼7-9 GPa coincides

with the significant reduction of the unit cell volume (∼10% at 1.5 GPa). This increases

the interaction strength between the atoms, which likely drives the increase in Tc. We will

discuss the unconventional mechanism of superconductivity in the family of FeTeSe crystals

in Section 3.2.2.

Finally, the largest enhancement in Tc was seen in monolayer FeSe films grown on

SrTiO3 substrates. In these devices, a superconducting gap was observed above 65 K

(Refs. [25–27]) and later confirmed by studies utilizing Angle Resolved Photoemission

Spectroscopy (ARPES) (Refs. [28, 29]) as well as in-situ four-probe measurements (Ref.

[30]). The physical origin of the drastic increase in Tc was the subject of intense investi-

gation, and, ultimately, it was suggested that the unusual pairing mechanism of FeSe is

enhanced by forward scattering electron-phonon interactions between FeSe and the SrTiO3

substrate, despite not being a typical BCS superconductor (Ref. [31]). This assertion

was backed by growing SrTiO3 with different oxygen isotopes, which modifies the strength

14



Figure 3.4: Tc enhancement by removing excess Fe atoms. The positions of excess Fe atoms
are shown to be at an interstitial location within the crystal. The magnetic susceptibility
and resistivity are shown as a function of temperature for the higher Fe concentration
(SC2, 11% excess Fe) and for the lower Fe concentration (SC1, 3% excess Fe). The lower
Fe concentration improves the diamagnetic response and the Tc of the crystal. Adapted
from Ref. [14].

of the electron-phonon interaction (extracted from ARPES measurements), resulting in

modifications to the size of the bandgap of FeSe.

15



Figure 3.5: The effect of oxygen annealing on removing excess Fe and improving the Tc.
The diamagnetic response, critical temperature, and critical current are all enhanced due
to the effective removal of excess Fe by oxygen annealing. Adapted from Ref. [19]

3.2.2 Fermi Surface/Pairing Mechanism/Pairing Symmetry

To understand the pairing symmetry in FeTeSe and the larger class of iron-based super-

conductors, I highly recommend the excellent perspective by Hoffman (Ref. [32]), which

I will follow here. In order to discuss the pairing symmetry in FeTeSe, it is instructive to

16



Figure 3.6: A phase diagram showing the pressure and temperature-dependent behavior
of FeSe. Specifically, the pressure-dependent enhancement of Tc can be seen until 10 GPa.
Afterward, this FeSe begins to undergo a transition to the hexagonal phase. Adapted from
Ref. [23]

discuss the Fermi surface in the larger class of iron-based superconductors. Specifically, in

the case of LaFeAsO1−xFx, Mazin et al. calculated the Fermi surface in the case of x = 0

(Fig. 3.7) and found that there were two electron cylinders centered on the M point and

two hole cylinders centered on the Γ point (Ref. [33]). There is also a heavy hole band at

the Γ point; however, Mazin showed that this went away at the relatively small doping of x

= 0.04 - 0.05. This Fermi surface turns out to be representative of a large number of iron-

based superconductors. It was further deduced by Mazin that these Fermi surfaces may be

similar enough to be linked by a small range of K vectors in the Brillouin zone. Two Fermi

surfaces linked by a common wavevector result in significant Fermi surface nesting, which

may give rise to a number of emergent phenomena. If superconductivity were mediated by

spin-fluctuations (a proposed pairing mechanism for the high Tc cuprate superconductors),

this would require the order parameter on the electron and hole pockets to have opposite

signs. This is denoted as S± pairing, as there is a change in the sign of the order parameter

between the two pockets (hence ±), but the order parameter is isotropic and nonzero in

each of the pockets (hence S). This is in contrast to the nodal order parameter in the d-wave

17



superconductivity of cuprate superconductors, which has multiple lobes.

Figure 3.7: The calculated band structure (a) and Fermi surface (b) of LaFeAsO1−xFx. The
key properties here are two electron cylinders around the M point and two hole cylinders
around the Γ point. Adapted from Ref. [33]

In the case of FeTeSe, the Fermi surface was experimentally verified by orbital-

polarization resolved ARPES (Ref. [34]). Further, the spin-fluctuation mediated super-

conductivity was confirmed using neutron scattering to measure the spin resonance in the

superconducting state of FeTe0.6Se0.4, which was found to be characterized by a wavevector

matching the Fermi surface nesting wavevector (Ref. [35]). Finally, the pairing symme-

try was confirmed by scanning tunneling microscopy (STM) (Ref. [36] using a technique

known as quasiparticle interference imaging (Ref. [37]). Typical STM measurements either

measure the tunneling current as a function of applied bias voltage (Fig. 3.8b), which can

reveal the superconducting gap, or map the tunneling current as a function of position

(Fig. 3.8a), which can reveal structures within the superconductor. In order to measure

quasiparticle interference, the ratio of the conductance at positive bias and negative bias

was mapped in order to probe particle-hole symmetric quasiparticles (Fig. 3.8c). A Fourier

transform was then applied to this mapping, giving rise to a map of the quasiparticle in-

tensity as a function of wavevector (Fig. 3.8d). Because the different wavevectors scatter

between pockets of the same sign or opposite sign, and the magnetic field induces vortices,

which may provide additional time-reversal-odd scattering, the intensity of scattering for

18



the different wavevectors should differ. This is seen in the experimental results, as q3,

which connects pockets of the same sign, is enhanced, and q2, which connects pockets of

opposite sign, is suppressed (Fig. 3.8e). This confirms the sign reversal of the order param-

eter between electron and hole pockets and, therefore, the S± pairing symmetry in FeTeSe

superconductors.

Figure 3.8: Quasiparticle interference probes of the unconventional superconductivity of
FeTeSe. a) The tunneling current as a function of position. b) The tunneling current as
a function of sample bias, showing the reduced tunneling current due to the quasiparticle
gap. c) The ratio of the conductance at positive and negative voltage bias as a function
of position. d) The Fourier transform of (c) showing the quasiparticle intensity vs the
wavevector. e) The quasiparticle interference under a magnetic field of 10 T showing
the enhanced or suppressed scattering based on the phase difference between the pockets,
confirming the S± pairing symmetry. Adapted from Ref. [37]

3.3 Topology

One aspect of FeTeSe crystals I have not yet touched on is the topological nature of the

electronic states in these crystals. This is central to the interest in FeTeSe as combined

19



topology and superconductivity give rise to Majorana bound states, which have been posed

as an attractive platform for quantum computing. I will begin by providing a brief histor-

ical and phenomenological survey of topological materials, which will follow the excellent

perspective by Moore (Ref. [38]).

At their simplest level, topological insulators are materials that possess linear-dispersion

(Dirac-like, i.e., graphene) electronic states at their surfaces when interfacing with non-

topological materials or media. Topological insulators get their name from the mathemati-

cal field of topology, which covers the properties of objects or spaces that can be smoothly

transformed between one another. Associated with this ‘smoothness’ is the topological in-

variant of the system. There is an old joke that a topologist can’t tell the difference between

a coffee mug and a doughnut. This classic example of topology is based on the idea that a

coffee mug can be smoothly deformed into a doughnut without tearing the surface, as both

objects have one hole, which serves as the topological invariant in this system. However,

transitioning from a ball to a doughnut would require an abrupt transition, i.e., tearing

the surface. In crystals, there are many different types of topological invariants, so I will

briefly cover the most straightforward examples.

The discovery of the quantum Hall effect, where 1D conductive edge states flow around

the edge of a 2D electron gas under external magnetic fields (Ref. [39]), led Haldane to

suggest that such an effect could be realized in crystals without an externally applied

magnetic field. This led to the idea of topological insulators, which were predicted (Ref.

[40]) and later shown to be realizable in a 2D quantum well, characterized by edge states

with quantized conductance, shown in Ref. [41]. In this system, the spin-orbit interaction

takes the place of the external magnetic field in producing the edge states. After this,

a 3D topological insulator was first realized in BixSb1−x, where the dispersion relation

of the surface states was revealed and a linear Dirac point was identified (Ref. [42]).

These topological surface states arose due to the opening of a band gap by the spin-orbit

interactions in these crystals, which induce band inversion.

20



I will now give a simplified description of what gives rise to topological surface states.

In a simple case of a topological crystal, spin-orbit coupling modifies energies in the band

structure of the material, and when spin-orbit coupling is strong, these bands can be

inverted in the bulk of the material. To match the symmetry of the bands at the interface

between a topological insulator and a normal insulator (or vacuum), the inverted bands

must revert to the uninverted case. In the process, these bands must cross the Fermi energy,

and therefore, electronic states are generated at the surface (Fig. 3.9). In reality, band

inversion is not the only requirement for a topological insulator, and the Berry curvature

should be calculated around a closed surface in the Brillouin zone, which classifies the

topological invariant of the material. Additionally, I have not touched on the symmetries

in these systems; the topological states in these systems can be protected by a number

of symmetries, such as time reversal symmetry (quantum Hall effect), as well as various

crystal symmetries. For a detailed discussion of topological materials, refer to Ref. [43].

Figure 3.9: Illustration of the band inversion effect giving rise to topological surface
states. The strong spin-orbit coupling opens a bandgap and causes twisting of the bands
(i.e., band inversion). At the interface with materials without band inversion, the bands
must be reverted to an untwisted non-inverted state and must cross to do so. This closes
the bandgap locally, giving rise to topologically protected surface states.

Now that a simple understanding of topological materials has been established, we

21



can touch on the suggested topology of FeTeSe, which is still being debated. Unlike in the

above examples, FeTeSe is not an insulating material in the bulk. Although the insulating

states in the bulk of topological insulators make the isolated measurement of the surface

states easier, the topological nature of the surface states is not dependent on an insulating

bulk of the material. Additionally, because both the topological states and the current

flow in superconductors happen at the surface, probes of the topology of FeTeSe are still

realizable, as will be shown next.

3.3.1 Topology In FeTeSe

The topological states in FeTeSe were first intensively investigated by Wang et al. (Ref.

[44]), who carried out first principle calculations of the band structure comparing the band

structure of FeSe and FeTe0.5Se0.5, as well as ARPES measurements of FeTe0.5Se0.5 crystals

to support their findings. Intuitively, the heavier Te atoms, as opposed to the lighter Se

atoms, would suggest an increased magnitude of spin-orbit coupling, due to the relativistic

nature of this effect. Therefore, one may imagine that as the content of Te is increased, the

topologically trivial FeSe may transition to a topologically non-trivial state in FeTe1−xSex.

Calculations of the band structure of FeSe and FeTeSe revealed similar structures, with

electron and hole pockets around the M and Γ points, respectively, as is typical for most

Fe-based superconductors. However, there is one clear difference between these two band

structures. Relative to the case of FeSe (Fig. 3.10a), in FeTeSe (Fig. 3.10b) the Γ2
−

band (bolded in red) is pushed down in energy, and along the Γ-Z direction now crosses

the Fermi energy, as well as other bands near the Fermi level. After this, the authors

added the spin-orbit interaction to their calculation (Fig. 3.10c), which reveals that one

of the crossings is avoided due to the spin-orbit interaction and a bandgap is opened (Fig.

3.10d). This avoided crossing mixes (often referred to as twists) the bands, similar to the

case of traditional 3D topological insulators, resulting in band inversion. They confirmed

a non-zero topological invariant, assuming a curved chemical potential represented by a

22



dashed line. Topological surface states can arise in non-insulating materials, and therefore,

utilization of a curved Fermi surface is necessary to exclude any effects of the chemical

potential crossing a band on the calculated Berry curvature. After this, the Γ2
− band

crossing the Fermi energy was confirmed by ARPES measurements taken as a function of

successive K doping of the FeTe0.5Se0.5 crystals.

Figure 3.10: First principles calculation of the band structure of FeTeSe, revealing band
inversion and a non-zero topological invariant. a) The band structure of FeSe. b) the band
structure of FeTeSe, neglecting the spin-orbit interaction. The main difference from FeSe
(a) is that the Γ2

− band (bolded in red) is pushed down in energy and crosses the Fermi
energy along the Γ-Z direction. c) The band structure of FeTeSe after adding the spin-orbit
interaction. d) A zoom-in on the Γ-Z direction showing the avoided crossing which gives
rise to the band inversion and topology in FeTeSe. Adapted from Ref. [44]

3.4 Topological Superconductivity

So, what is the significance of topological surface states in FeTeSe? This significance is

related to Majorana bound states, which can emerge when superconducting and topologi-

cal systems are combined, and may have applications in topologically protected quantum

computation due to their unique exchange statistics. Below, I will give a brief overview

23



of Majorana Fermions, Majorana-bound states, and a simple description of the exchange

statistics. For a more in-depth discussion, please refer to the referenced articles.

The term Majorana Fermion refers to a Fermion which is its own antiparticle, and

was originally proposed in the context of particle physics. Because particles and antipar-

ticles must have opposite charge, a Majorana Fermion, which is its own antiparticle, must

have zero charge. In superconducting systems, electron-hole symmetry is imposed by the

superconducting condensate, and quasiparticle excitations that are combinations of elec-

tron and hole creation operators can be generated (Ref. [45]). These quasiparticles are

commonly referred to as Bogoliubov quasiparticles. Among the Bogoulibov quasiparticles

in a typical superconductor, a Majorana Fermion may be generated if a quasiparticle is

its own antiparticle. In order to realize such a quasiparticle, the normal electron states

in the superconductor must follow a linear Dirac-like dispersion, according to Ref. [46].

Based on this idea, in 2008, breakthrough theoretical works by Fu and Kane (Refs. [47,

48]) suggested that a superconductor coupled to the linear dispersion of electron states in a

topological insulator could realize Majorana bound states. They demonstrated that these

Majorana bound states would exhibit non-Abelian exchange statistics that would make

them useful for quantum computation.

A brief note on exchange statistics: Abelian exchange statistics are what describe

typical Fermions and Bosons, which accrue a complex phase eiϕ in the wavefunction when

two particles positions are exchanged, where eiϕ will be 1 for Bosons (due to the symmetric

wavefunction) and -1 for Fermions (due to the antisymmetric wavefunction). Non-Abelian

exchange statistics imply that when two particles are exchanged, a phase is accrued and,

critically, the mode of the wavefunction is modified as well. Further, the non-abelian

exchange statistics imply the wavefunction depends on the order in which particle exchanges

are performed and the rotation direction of the exchange. Since the wavefunction can be

controlled this way, a method of entanglement known as braiding was proposed as a basis

for qubits. Figure 3.11 shows a schematic of Majorana braiding where the qubit is initially

24



in the ground state (|012034⟩) and finally in a superposition of the ground and excited state

((|012034⟩+ |112134⟩)/
√
2).

Figure 3.11: Illustration of braiding operations on Majorana bound states. The Majo-
rana wavefunction starts in the ground states defined by pairs of Majorana particles. By
exchanging the particles’ positions, the wavefunction will now be in a superposition of the
ground and excited states. For successive braiding operations, the order of exchanges af-
fects the final state. Adapted from Ref. [43]

3.4.1 Topological Superconductivity in FeTeSe

Along with the prediction of surface states in FeTeSe by Wang et al. (Ref. [44]), the

author also noted that the combination of topological surface states and superconductivity

in a single material (FeTeSe) could give rise to Majorana bound states on the surface of

FeTeSe. The superconducting quasiparticle gap ∆, however, will ‘gap out’ these surface

states, making them inaccessible to experimental probes. Fortunately, the order param-

eter (and therefore the quasiparticle gap) becomes zero at the core of Abrikosov vortices

(Fig. 3.12). Therefore, it was predicted that Majorana bound states could be bound to

25



the cores of Abrikosov vortices in topological superconductors (Refs. [47, 49]). ARPES

measurements were able to prove topological superconductivity in FeTeSe by imaging the

spin-polarized Dirac-like surface states of FeTe0.55Se0.45 as well as proving the s-wave nature

of the superconductivity (Ref. [50]).

Figure 3.12: Illustration of a vortex in a superconductor. The order parameter (ψ) is
reduced inside a radius equal to the coherence length (ξ), eventually becoming zero at the
core of the vortex. The magnetic field intensity (H) decays over the penetration depth of
the superconductor (λ).

That same year, the first direct experimental probe of Majorana bound states in

FeTeSe was achieved (Ref. [51]). This was achieved using STM, which we discussed above

for the determination of the pairing symmetry. STM locally probes the density of states

as a function of energy by measuring the tunneling conductance from an atomically sharp

tip as a function of bias voltage. Additionally, STM is able to resolve spatial features with

a resolution smaller than 0.1 nm, which allows spatial probing on the atomic scale, and is

much smaller than the nm scale vortices. With these advantageous properties Wang et al.

(Ref. [51]) were able to image vortices on the surface of FeTe0.55Se0.45 under an applied

magnetic field of 0.5 T. The tunneling conductance was then measured as a function of

energy at the center of the vortex and at the edge of the vortex (Fig. 3.13). These

measurements reveal a zero-bias peak in the conductance at the center of the vortex, a

signature of tunneling through the Majorana bound states, which are predicted to occur at

zero energy (Refs. [47–49]). The author also ruled out Caroli de Gennes Matricron (CdGM)

26



Figure 3.13: A direct probe of Majorana bound states at the core of a superconducting
vortex using STM. A peak in the conductance can be seen at the core of the vortex using
STM (a). This peak in the conductance can be shown to be centered on zero energy, as well
as at the core of the vortex (b). An insensitivity to magnetic field was also demonstrated,
ruling out CdGM states and Kondo resonances (c,d). Adapted from Ref. [51]

states (Ref. [52]) and Kondo resonances (Ref. [53]), which can occur at low energies and

masquerade as Majorana bound states. In the case of CdGM states, these are predicted to

occur at discrete energy levels of µ∆2/EF for µ = 1/2, 3/2, 5/2, ... (Ref. [52, 54]). However,

the most convincing evidence is that CdGM states should split as a function of space when

moving away from the vortex center (Ref. [55]), this behavior was not observed, see Fig.

3.13b. In regard to Kondo resonances, these tunneling states would typically take place

at a magnetic impurity, and as a function of applied magnetic field, should split in energy

(Ref. [56]), which was also not observed (Fig. 3.13c,d).

27



3.4.2 Higher Order Topological Superconductivity in FeTeSe

So far, we have discussed topological materials in which the topological states exist with

dimensions N − 1, where N is the dimension of the parent material (1D edge states in 2D

Electron gases, 2D surface states in 3D topological insulators). However, it is possible to

have what is known as a higher-order topological insulator, where topological states can

exist in N − 2 (1D edge modes in a 3D platform) or N − 3 dimensions (0D bound states

in a 3D platform). Zhang, Cole, and Das Sarma (an early pioneer of topological supercon-

ductivity) predicted that higher order topological superconductivity could potentially be

realized in FeTeSe, due to the combination of 2D topological surface states and anisotropic

S± pairing symmetry (Ref. [57]). They showed that the anisotropy would result in surface

states on the top surface with a sign reversal of the pairing potential compared to the side

surfaces. Due to the sign reversal of the pairing potential, there must be an angle where

the pairing potential passes through zero, and therefore, the superconducting gap is closed,

resulting in 1D helical hinge Majorana zero modes. Fig. 3.14 from Ref. [58] schematically

shows how topology and S± superconductivity come together to realize this phenomenon.

Figure 3.14: Visualization of the S± superconductivity on the surfaces of FeTeSe, and
the resulting helical hinge zero modes. The closing of the superconducting gap at an angle
between the two surfaces of FeTeSe and the topological surface states give rise to the higher
order topology in this material. Adapted from Ref. [58].

That same year, Gray et al. confirmed the existence of these helical hinge zero modes

(Ref. [58]). They fabricated two types of contacts to FeTe0.55Se0.45, (1) using a hexagonal

28



boron nitride insulating layer to block the hinge so the electrode only touches the top

surface, and (2) contacting both the hinge and the top surface. They found a sharp peak in

conductance at zero bias in the sample contacting the edge, which was absent in the contact

to the top surface (Fig. 3.15). Additionally, they demonstrated that this peak likely does

not arise from Andreev bound states by showing that the temperature dependence differed

from what would be expected of Andreev bound states (∝ 1
T
). The discovery of helical

hinge Majorana zero modes in FeTe0.55Se0.45 provides further evidence of the S± pairing

symmetry, as gap anisotropy is necessary to realize these higher-order topological states.

Figure 3.15: a-c) A transport study on FeTeSe (a) revealing a zero bias conductance peak
when the electrode is in contact with the edge of the sample (c), which is absent when just
contacting the top surface (b), confirming the presence of helical hinge zero modes. The
small peak in (b) is likely due to tunneling through the hBN into the helical hinge zero
mode, which exists at zero energy. Adapted from Ref. [58].

3.5 Josephson Effects in FeTeSe-Based Devices

Although we will discuss the specifics of Josephson junctions in the following Chapters, I

will now give an overview of the current research that has been conducted on FeTeSe-based

Josephson junctions. The first study revealing Josephson effects in FeTeSe was performed

by Wu et al. (Ref. [59]). In their study, they fabricated FeTeSe-based constriction junctions

using a focused ion beam to etch the FeTeSe down to widths ranging from ∼250 nm to

29



∼650 nm (Fig. 3.16a). In these devices they measured Shapiro steps matching the predicted

height (Fig. 3.16b), as well as large induced gaps of up to 2 meV, determined by the IcRn

product and the Ambegaokar-Baratoff relation, described in Ref. [60] (see chapter 5 for

a more detailed discussion of the Ambegaokar-Baratoff relation). Another FeTeSe-based

Josephson junctions was produced by Qiu et al. by stacking two FeTeSe crystals on top

of one another (Fig. 3.17a). In this device they measured a number of novel properties,

but most relevant to this study was the unusual dependence of the critical current on the

magnetic field (Fig. 3.17b). This unusual dependence appears to be a mix of a 0-Junction

(the typical case) and a π-Junction (typically only in systems with magnetic materials or

multiband superconductors). They suggested that these effects arise due to ferromagnetism

at the interface between the two FeTeSe flakes. However, they pointed out that excess Fe,

which would be the most obvious cause of the interfacial ferromagnetism, is not likely

driving the ferromagnetic behavior in these devices, as the hysteresis effects disappeared

above the superconducting critical temperature of FeTeSe.

Figure 3.16: a) A constriction Josephson junction fabricated from FeTeSe crystals. b)
Shapiro steps were reliable in this system, confirming the realization of a Josephson junction
in this device. Adapted from Ref. [59].

30



Figure 3.17: a) A FeTeSe-FeTeSe homojunction where the vdW gap between he crystals
allows for tunneling between the FeTeSe flakes. b) The complicated magnetic field depen-
dence of the critical current, showing asymmetry in B and a minimum close to zero. c) The
description for the unusual magnetic field dependence is a combination between 0-junction
behavior (the typical case) and π-junction behavior (arising in Josephson junctions with
multiband superconductors or magnetic insulating layers). Adapted from Ref. [61].

31



Chapter 4

Josephson Junctions

4.1 Josephson Physics

Josephson junctions are devices where two superconducting electrodes are separated by

a thin non-superconducting region (Ref. 4.1). When the non-superconducting region

is thinner than the relevant coherence length (the superconductor coherence length in a

superconductor-insulator-superconductor junction and the normal metal coherence length

in a superconductor-normal metal-superconductor junction), there will be tunneling of

cooper pairs between the superconducting banks. As a consequence of the phase-coherent

transport, Josephson junctions demonstrate zero resistance for pair tunneling at zero bias

voltage, but finite resistance (in general) at finite bias. Brian Josephson first described

the governing equations of Josephson junctions in 1962, which are known as the Josephson

equations (Ref. [62]). Below, we will discuss the derivation of the Josephson equations as

well as the primary phenomena observable in this system.

4.1.1 Derivation of Josephson Equations

As Ginzburg-Landau theory demonstrates, each of the superconducting electrodes in a

Josephson junction can be described by a macroscopic wave function, respectively.

32



Figure 4.1: Schematic of a Josephson junction showing the macroscopic wavefunction of
each superconducting electrode.

ψ1 =
√
n1e

iφ1 (4.1)

ψ2 =
√
n2e

iφ2 , (4.2)

where φ1 and φ2 are the macroscopic phases of the first and second superconducting

electrodes, respectively, and n1 and n2 are the densities of Cooper pairs. We will later

assume the electrodes are identical for simplicity; however, the electron densities must first

be handled independently, as the charge passing from one electrode to the other will be

represented by ṅ1 or ṅ2. This does not violate n1 = n2, because our system is attached to

a battery, so the electrodes will not become charged by a finite ṅ1 or ṅ2. These equations

do not explicitly account for the battery as a charge source or sink; therefore, this must be

handled through a reasonable assumption which I will cover later.

The time-independent Schrodinger equation for a two-level system can be used to

describe the coupling between the two electrodes, where the ground state energy U char-

acterizes zero coupling between the two superconductors and the excited state energy K

characterizes the coupling energy between the two electrodes. Because we will apply a

voltage V between the two superconducting electrodes, we can assume U1 = +V/2 and

U2 = −V/2. For now, we exclude the contribution of magnetic fields.

iℏ
dψ1

dt
=
qV

2
ψ1 +Kψ2. (4.3)

33



iℏ
dψ2

dt
= −qV

2
ψ2 +Kψ1. (4.4)

Substituting the wavefunction of each electrode into the time-dependent Schrodinger equa-

tion results in the equations

iℏ(
√
ṅ1 + iφ̇1

√
n1)e

iφ1 =
qV

2

√
n1e

iφ1 +K
√
n2e

iφ2 , (4.5)

iℏ(
√
ṅ2 + iφ̇2

√
n2)e

iφ2 = −qV
2

√
n2e

iφ2 +K
√
n1e

iφ1 . (4.6)

By equating the real and imaginary parts of each equation, we arrive at four equations.

Where we have defined the phase difference between the junction as δ = φ1 − φ2.

ṅ1 =
2K

ℏ
√
n1n2 sin(δ) , ṅ2 = −2K

ℏ
√
n1n2 sin(δ), (4.7)

φ̇1 =
K

ℏ

√
n2

n1

cos(δ)− qV

2ℏ
, φ̇2 =

K

ℏ

√
n1

n2

cos(δ) +
qV

2ℏ
. (4.8)

Where we can see that

ṅ1 = −ṅ2. (4.9)

This represents the transport of Copper pairs between the electrodes, and as such, we can

write

J =
2K

ℏ
√
n1n2 sin(δ) = ṅ, (4.10)

where J is the current density. Now we can make the reasonable assumption that n1 = n2,

based on the idea that the Josephson junction is connected to a battery that will source

or sink the charge in each electrode as the current flows through the junction. With this,

we can additionally define Jo =
2K
ℏ n1. This is the critical current density of the Josephson

junction, and is analogous to the critical current density of a superconductor on a simple

34



level. Using this definition, the first Josephson equation can be written as

J = Jo sin(δ). (4.11)

By subtracting the equations in Eq. 4.8, and using our previous definition for the phase

difference between the superconductors, we can write the second Josephson equation

δ̇ =
2eV

ℏ
, (4.12)

where we have substituted q = 2e for the Cooper pair. And its time-integrated form.

δ(t) = δ0 +
2e

ℏ

∫
V (t)dt (4.13)

The result of this equation is that if a finite DC voltage is applied across the junction, the

phase will change at a constant rate, given in Eq. 4.12, causing oscillations of the current

(Eq. 4.11), and there will be no net current flow from the superconducting state. In real

devices, there will be conduction due to quasiparticles at this point, however, they are not

treated within this model. A typical current-voltage curve, as measured by Shapiro et al.,

is shown in Fig. 4.2, where the voltage was swept (y-axis) and the tunneling current was

measured (x-axis).

In comparison, if a small current less than Jo is driven through the junction, then there

will be a constant finite phase difference between the superconducting electrodes, given by

Eq. 4.11. From Eq. 4.12, this would mean that the voltage across the junction must be

zero. Driving a current instead of a voltage is referred to as a current-bias measurement

and is discussed in detail in Sec. A.1.2.

35



Figure 4.2: A typical current-voltage curve, where current is shown on the x-axis and
voltage is shown on the y-axis, adapted from Ref. [63].

4.1.2 Shapiro Steps

Only one year after Josephson’s landmark publication, Sidney Shapiro measured the ex-

istence of finite jumps in the current-voltage curve in a Josephson junction irradiated by

microwave photons (Ref. [63]). We will next discuss this phenomenon in detail.

Due to the microwave photons irradiating the sample, the voltage across the junction

can be expressed as the sum of the DC voltage V0 and the AC voltage V1,

V = V0 + V1 cos(ω1t). (4.14)

Substituting this into the integral form of the second Josephson equation ( Eq. 4.13) results

36



in the equation

δ(t) = δ0 +
2eV0
ℏ

t+
2eV1
ℏω1

sin(ω1t). (4.15)

Substituting this into the first Josephson equation (Eq. 4.11), results in the equation

J = Jo sin

(
δ0 +

2eV0
ℏ

t+
2eV1
ℏω1

sin(ω1t)

)
. (4.16)

Equations of the type sin(sin(x)) can be expanded as a sum of Bessel functions, resulting

in the equation

J = Jo
∑

(−1)nJn

(
2eV1
ℏω1

)
sin

(
γ0 +

2eV0
ℏ

t− nω1t

)
, (4.17)

where Jn is the nth Bessel function of the first type. The current will oscillate with time

and average out to zero unless nω1 =
2eV0

ℏ is satisfied. At which point, there will be a DC

contribution for the nth term in the series. As a result, if the voltage is increased, there

will be no increase in current until

V0 =
nℏω1

2e
=
nhf

2e
, (4.18)

where the applied frequency f is typically in the range of GHz, and the voltage steps

correspond to ∼ 2µV/GHz. Similarly, if a current is applied to the junction, the voltage

will remain constant until sufficient current exists to drive the voltage to jump to the nth

step, shown in Fig. 4.3. This results in finite jumps in the current-voltage curves known

as Shapiro steps, shown in Fig. 4.3.

Deviations from the typical Shapiro step behavior can be used as a probe of the

properties of Josephson junctions. For example, voltage jumps occurring at fractional

values of the Shapiro steps can indicate deviations from the typical current-phase relation

(δ̇ = 2eV
ℏ ). Specifically, higher frequency sinusoidal contributions to the current-phase

relation can arise in highly transparent Josephson junctions, as is shown in Ref. [64].

37



Another example is the missing odd-value Shapiro steps, which are predicted to arise in

the presence of Majorana bound due to the 4π period current phase relationship (Refs.

[65, 66]). However, missing odd Shapiro steps have been observed in topologically trivial

Josephson junctions as well (Ref. [67]), and therefore this is not direct evidence of Majorana

bound states.

Figure 4.3: Diagram of Shapiro step behavior of a Josephson junction.

An important note about the current-voltage curves: As Tinkham notes in Chap-

ter 6.3.4 of Introduction to Superconductivity (Ref. [1]), the above model assumes that

a voltage is applied to the sample and that the current is measured. This is known as

a voltage-bias measurement and gives rise to the relatively simple solutions shown above.

However, in realistic cases, due to the zero resistance of the superconductor, the finite

38



resistance in the rest of the circuit sets the current through the Josephson junction, ef-

fectively rendering the measurement a current-bias measurement (where current is applied

and the voltage is measured). For this reason, current bias measurements are often used

to measure Josephson junctions (see the Appendix A.1.2 for a more in-depth discussion of

the advantages of current-bias measurements). In the case of current bias measurements,

an analytical solution similar to Eq. 4.17 can not be obtained and, therefore, numerical

solutions are required. Numerical solutions show that finite DC currents can exist for volt-

ages other than the Shapiro step heights (Refs. [68, 69]), such as between the Shapiro step

plateaus, as is shown schematically in Fig. 4.3.

4.1.3 Magnetic Field Dependence of Josephson Junctions

I will now address the contribution of the external magnetic fields on the behavior of

the Josephson junction. A brief summary of the derivation I will follow: I will look at the

modification of the critical current in a short Josephson junction (relative to the penetration

depth) in an applied magnetic field. In order to calculate the critical current, I use the gauge

invariant phase difference across the junction. The dependence of the gauge invariant phase

difference on the magnetic field can be derived by setting the sum of the order parameter

around the loop equal to zero. After this, the order parameter is eliminated from the

expression and a relationship between the gauge invariant phase and the magnetic field si

obtained. We can imagine a Josephson junction comprising two superconductors separated

by a thin non-superconducting material of thickness d, shown in Fig. 4.4. A spatially

uniform magnetic field, B⃗ = Bŷ, is then applied in the y-direction, perpendicular to the

direction of the current flow (in the z-direction).

Due to the applied magnetic field, the phase difference across the junction, which will

determine the supercurrent, is now the gauge invariant phase difference γ. Unlike the order

parameter, γ will vary across the length of the junction (x-direction) under an applied

magnetic field, which we will see later. The gauge invariant phase difference across the

39



Figure 4.4: Diagram showing the magnetic field incident on a Josephson junction and the
closed loop utilized to determine the magnetic field dependence.

Josephson junction is

γ(x) = φ2 − φ1 −
2π

Φ0

∫ 2

1

A · dl (4.19)

−γ(x+∆x) = φ4 − φ3 −
2π

Φ0

∫ 4

3

A · dl, (4.20)

where A is the vector potential due to the external magnetic field, and the minus sign on

γ in the second equation is because the integral is in the opposite direction as the gauge

invariant phase difference, which is defined from the left electrode to the right electrode.

Φ0 is the magnetic flux quantum and is defined by Φ0 = h
2e
. According to the London

equations, in the electrodes

∇φ =
2π

Φ0

(ΛJ + A). (4.21)

However, because we choose to take our path deep within the electrodes J = 0. Finally,

in order to calculate the phase difference between the superconducting electrodes, we can

first consider the phase around the entire loop, which must be single valued mod(2π) as

this is the order parameter characterizing the superconductor. This can be represented by

40



the integral of the phase gradient around the loop

∫
∇φ · dl = (φ2 − φ1) + (φ3 − φ2) + (φ4 − φ3) + (φ1 − φ4) = 0. (4.22)

Which can also be written as

∫
∇φ · dl = (φ2 − φ1) +

∫ 3

2

∇φ · dl + (φ4 − φ3) +

∫ 1

4

∇φ · dl = 0. (4.23)

Substituting Eqs. 4.19, 4.20 and 4.21 into Eq. 4.32 the order parameter can be eliminated

to yield

γ(x) +
2π

Φ0

∫ 2

1

A · dl+ 2π

Φ0

∫ 3

2

A · dl− γ(x+∆x) +
2π

Φ0

∫ 4

3

A · dl+ 2π

Φ0

∫ 1

4

A · dl = 0, (4.24)

which is equivalent to

γ(x+∆x)− γ(x) =
2π

Φ0

∮
A · dl. (4.25)

Resulting in the equation,

γ(x+∆x)− γ(x) =
2πΦ

Φ0

, (4.26)

where the flux can be represented by the area of penetration of the magnetic field Φ = BA,

with A = (d + 2λ)∆x. The penetration depth is incorporated in the thickness of the

junction as the magnetic field will also penetrate this region. This results in the equation

γ(x+∆x)− γ(x)

∆x
=

2π

Φ0

B(d+ 2λ), (4.27)

which as ∆x goes to 0 becomes

dγ

dx
=

2π

Φ0

B(d+ 2λ). (4.28)

41



Integrating this equation yields the gauge invariant phase difference as a function of x

γ(x) =
2π

Φ0

B(d+ 2λ)x+ γ0. (4.29)

Therefore, the current density in the junction will have a spatial dependence according to

J = J0 sin

(
2π

Φ0

B(d+ 2λ)x+ γ0

)
, (4.30)

which, under the assumption of a homogeneous critical current J0, can be integrated over

the length of the junction L to get the total current flowing through the junction

I = I0 sin(γ0)
sin

(
πΦ
Φ0

)
πΦ
Φ0

, (4.31)

where Φ = B(d + 2λ)L. The current has a maximum value at γ0 = π/2, resulting in the

usual Fraunhofer diffraction pattern for the maximum current, shown in Fig. 4.5, given by

Imax = I0

∣∣∣∣∣∣
sin

(
πΦ
Φ0

)
πΦ
Φ0

∣∣∣∣∣∣ . (4.32)

It should be noted that this calculation was done neglecting self-field effects, which

become significant when L > λJ , where λJ =
√

Φ0

2πµ0(d+2λ)Jc
, and is defined as the Josephson

penetration depth.

42



Figure 4.5: Plot of the Fraunhofer pattern showing the normalized critical current as a
function of the magnetic flux.

43



Chapter 5

FeTeSe-Al Josephson Junction

We fabricated devices based on the interface between Al and FeTe0.55Se0.45, a material

which provides a compelling platform for investigating phenomena associated with uncon-

ventional superconductivity. In this system, Josephson effects were observed, which deviate

from the typical behavior of Josephson junctions shown in Section 4.1. For each of the un-

usual features seen, I will present the data step by step to highlight the atypical features

demonstrated. For each of the unusual phenomena, I will discuss potential mechanisms

driving the behavior. Ultimately, we find that the Josephson effects present in this system

may arise from a phase slip line induced in FeTe0.55Se0.45 instead of the expected Josephson

junctions at the Al-FeTe0.55Se0.45 interface.

5.1 Fabrication and Measurements

5.1.1 Fabrication

Before diving into the results, I will give a brief description of the fabrication and mea-

surements of our devices, shown schematically in Fig. 5.1. In order to produce flakes of

FeTe0.55Se0.45, which we can process using standard chip processing techniques, we first

take bulk crystals of FeTe0.55Se0.45 and exfoliate them by the scotch tape method. The

44



Figure 5.1: a-f) Overview of the fabrication process of the Al-FeTeSe devices. First exfo-
liation of the FeTeSe was performed (a), followed by spinning of an e-beam resist (b). A
device pattern was then written into the e-beam resist and developed (c). Titanium/A-
luminum 5 nm/50 nm was deposited by magnetron sputtering (d), and the excess Al was
removed during the liftoff stage (e). This process was then repeated for Ti/Au 5 nm/ 50
nm, using electron beam deposition instead of sputtering.

adhesive force of the scotch tape is stronger than the weak inter-layer vdW force holding

the 2D layers of FeTe0.55Se0.45 together. As a result, when the tape is peeled apart, the

FeTe0.55Se0.45 crystal are cleaved. This tape is then applied to a clean substrate composed

of conductive p-doped silicon capped with 285 nm SiO2. Moderate pressure was applied

and the sample was given approximately 5 minutes to ensure the FeTe0.55Se0.45 interfaces

45



the substrate well. After this, the tape is peeled back from the substrate and flakes of

FeTe0.55Se0.45 will be cleaved by the adhesive force of the substrate and the tape (Fig. 5.1

a), leaving flakes of FeTe0.55Se0.45 approximately 1-10 µm wide and 10-100 nm thick. After

flakes have been produced, electron beam resist (PMMA 950A4) can be spun onto the

substrate and baked at 180 ◦C for 2 mins (Fig. 5.1b). Alignment marks are then written

by electron beam lithography, and subsequently developed in a 3:1 mixture of isopropanol

(IPA):methyl isobutyl ketone (MIBK). Optical images of the sample and alignment marks

are then used to locate the position of the flake on the chip exactly, and then the intended

electrodes can be patterned by electron beam lithography as well (Fig. 5.1c). In the case

of our devices, there were two lithography and deposition steps. Aluminum electrodes were

deposited by Magnetron Sputtering and Au electrodes were deposited by Electron Beam

Deposition, where, in both cases, a thin adhesion layer of ∼5 nm Ti was used (Fig. 5.1d).

See Appendix A.5 for standard operating procedures, maintenance, and modifications to

the Magnetron Sputtering system and the Electron Beam Deposition system. After metal

deposition, the PMMA is removed by acetone, and therefore the metal on the surface of

the PMMA is removed as well (Fig. 5.1e). This process is repeated for Au electrode (Fig.

5.1f). The resulting device is shown schematically in Fig. 5.2 and the device image is

shown in Fig. 5.3. The area of the electrode-FeTeSe interface is ∼ 1.8 µm2.

5.1.2 Measurement Procedures

After device fabrication, the substrate was affixed to a small sample holder using PMMA

glue, which was then affixed to a larger sample holder by vacuum grease. At this point,

the electrodes on the device were connected to the electrodes on the sample holder by wire

bonding (See Appendix A.3 for details of wire bonding). One of the electrodes is also

connected to the bonding pad corresponding to the RF lines. This allows measurement of

the samples using a Lock-in 4-terminal current-bias measurement scheme (shown in Fig.

5.4), while irradiating the sample with RF photons using Rhode and Schwarz SMB100A

46



Figure 5.2: Schematic and dimensions of FeTeSe device showing the side view and top
view. The FeTeSe flake is ∼1.8 µm wide and the Al electrode is ∼1.0 µm wide. The
intended device was at the Al-FeTeSe interface, which has an area of 1.8 µm2, however we
will see that other regions in the device can potentially contribute as well.

microwave signal generator. Frequency ranging from 100 MHz to 7 GHz and an applied

RF power ranging from -70 dBm to 5 dBm were used throughout the measurements. The

real incident RF power on the device was likely reduced by greater than 10 dB due to

attenuators in the lines. The specifics of 4-terminal measurements are discussed in Ap-

pendix A.1.2. The four terminal measurement scheme isolates the voltage drop across the

Al-FeTe0.55Se0.45 interface (nominally including a Ti layer) from the voltage drop across

the lines and other interfaces in the system (voltage drops across the small strips of Al

and FeTe0.55Se0.45 comprising the electrodes could still be measured). After wire bonding,

the samples are then loaded into either a Leiden Dilution refrigerator or an Oxford Instru-

ments Dilution Refrigerator, which were utilized to achieve temperatures of ∼50 mK and

∼25 mK, respectively. See Appendix A.1.3 for details of DC and RF wiring.

47



Figure 5.3: Optical image of the FeTeSe device structure showing the electrodes used for
the four-terminal measurement. This four-terminal measurement should isolate the voltage
drop across the Al-FeTeSe interface, and a small amount of the FeTeSe and Al materials
as well, which we will see can potentially have a significant impact. This measured region
is circled in red.

48



Figure 5.4: Circuit schematic of the measurement technique used to investigate the device;
the 4-terminal current-bias measurement with a DC voltage source and an RF source. The
lock in amplifier produced a low frequency AC voltage excitation which we convert into
a current excitation I+ using a bias resistor. The lock-in then measures the differential
resistance dV

dI
in Ohms using a phase locked technique. This resistance was then measured

as a function of DC current using a voltage source and a bias resistor, and as a function of
RF frequency and power (using a SMB100A microwave signal generator). See Appendix
A.1.2 for a more detailed discussion of the measurement methods.

49



5.2 Inner and outer junction effect

When measuring a Josephson Junction, the differential resistance (dV/dI) vs current mea-

surement resembles measurements of a superconducting flake, but with a significantly re-

duced critical current. We therefore expect to measure zero resistance at zero bias current

and a resistive state emerging at higher currents. We measured this phenomenon in our

Al-FeTeSe Josephson junction at a base temperature of ∼50 mK, shown in Fig. 5.5a.

Figure 5.5: a,b) Initial dV
dI

vs I measurements of the FeTeSe device. An initial jump from
a 0 Ω state to a 3 Ω resistance state occurs around 0.25 µA (a). Two other distinct jumps
in resistance can be seen at 6 µA and 13 µA. We will later find Josephson effects emerginf
for both the jump at 0.25 µA (the inner junction) and at 6 µA (the outer junction). The
resistance jump at 13 µA likely corresponds to the bulk Al electrode, which will be shown
later.

We can clearly see there is a nearly zero resistance state around zero bias current,

and a critical current of approximately 0.25 µA, beyond which the differential resistance

jumps to approximately 3 Ω (Fig. 5.5a). Expanding the range of our DC current sweep to

20 µA reveals that there is another jump in resistance to approximately 16 Ω occurring at

a current of 7.5 µA (Fig. 5.5b). This is typical for Josephson junctions, as the electrodes

50



also have a critical current beyond which there will be a jump in the differential resistance.

We will see later see, however, that other effects can also give rise to multiple jumps in

resistance. There is a large jump in the resistance around 13 µA likely arising from the

transition to the