1. Point Contact Spectroscopy on FeTe0.55Se0.45, Pb, and YFe2Al10: An Undergraduate
Investigation into Quantum Criticality
Amanda M. Landcastle*
Department of Physics – University of Illinois at Urbana-Champaign
Abstract
A quantum theory of point contact spectroscopy (PCS) was recently developed as a potential
filter for non-Fermi liquid behavior in correlated materials. Classically, PCS is an experimental
technique which has been used for several decades to determine scattering information on
normal metals as well as gap information on superconducting materials. The quantum theory
of PCS for correlated materials suggests that a zero bias peak in the dI/dV spectrum can be
associated with an excess density of states for non-Fermi liquids. This report gives the initial
experimental approach to using PCS on YFe2Al10 in order to try to detect quantum critical
fluctuations in this material.
I. Introduction
Superconductivity is characterized by zero
resistance and perfect diamagnetism below a
critical temperature, Tc. Through the
techniques used to characterize
superconductors, a theory was developed
pertaining to these same techniques being
used to identify an effective density of states
caused by non-Fermi liquid behavior1
. In
normal metals, the interactions between the
electrons can be ignored without interpreting
the system incorrectly. In correlated
materials, these interactions must be
accounted for because a more complicated
description of the system is necessary. Point
contact spectroscopy (PCS), also known as
quasiparticle scattering spectroscopy (QPS),
has been used for several decades to
determine spectroscopic information of the
electronic scattering in metals, providing
information regarding electron-phonon
coupling, magnons, and Kondo scattering2
.
PCS has also been used to resolve the energy
gap of a superconductor via analysis of
Andreev reflection3,4
. More recently, PCS
has been shown to detect electron nematicity
in the normal state for some iron-based high
temperature superconductors5
. A quantum
theory was recently developed suggesting
that PCS is capable of measuring the density
of states arising from non-Fermi liquid
behavior, common in correlated materials1
.
This means that if a theorized signature peak
at zero bias is present, the material could be
determined to have non-Fermi liquid
behavior. This paper introduces the
experimental approach to determine if PCS
is able to identify certain correlated systems
known as quantum critical materials.
PCS uses a modulation technique to measure
the derivatives of the current-voltage (I-V)
characteristics of materials. This is done by
supplying the sample with a dc-current and
an ac-current at a frequency ω. A dc-voltage
created on the sample is measured and a
preamplified ac-voltage is recovered at ω or
2ω, which are proportional to the first
derivative (dV/dI) and second derivative
(d2
V/dI2
) of the I-V curve, respectively. So,
when a linearly increasing current is supplied
to the junction, the first and second
derivatives are directly measured2
. Two
electrodes are placed on the sample of
interest, serving as positive current and

2. voltage leads. Two electrodes in metallic
contact with each other serve as the negative
current and voltage leads and that is called
the point contact. As the scattering processes
take place within the sample, spectroscopic
information is obtained. All metallic contact
have specific regimes of electronic transport
which dictate the usefulness of the
spectroscopic information obtained from the
process. These regimes are shown in Figure
1. A contact in the ballistic regime has
parameters such that 𝑙 𝑒𝑙 ≫ 𝑑 and charge
carriers can transport current with minimal
scattering. Being within this limit allows
spectroscopic information to be detected. In
the diffusive regime, the contact has the
parameters such that 𝑙 𝑒𝑙 < 𝑑 < √𝑙 𝑒𝑙 × 𝑙𝑖𝑛. In
this regime, there is elastic scattering that
takes place which results in weak
spectroscopic information. If a contact is in
the thermal or Maxwell limit, the contact size
is described by 𝑙𝑖𝑛 ≪ 𝑑. In this regime, large
amounts of scattering occurs in the junction
area. Energy is lost to joule heating and
spectroscopic information is smeared5
.
Point Contact Andreev Reflection (PCAR)
spectroscopy focuses on measuring the
superconductor energy gap and its symmetry
through Andreev reflection. Andreev
reflection occurs when in the ballistic regime
between a normal metal and a
superconductor and is observed in spectra as
an excess conductance, typically double
peaked for conventional superconductors,
centered at zero bias. The energy gap is an
interval in the electronic density of states of
a superconductor between the occupied and
unoccupied states with forbidden energy
levels. This gap represents the minimum
energy required for an electron-like or hole-
like quasiparticle to excite from a relaxed
state and is determined by
𝐸𝑔 =
7
2
𝑘 𝐵 𝑇𝑐
where kB is Boltzmann’s constant. When an
electron tries to cross into the forbidden
region, it can get retroreflected back into the
metal as a hole, creating a Cooper pair in the
superconducting condensate, which is then
“allowed” to propagate through the gap. In
conventional superconductors, Cooper pairs
originate from electron-phonon coupling.
When an electron interacts with the lattice of
a material due to the Coulomb attraction, the
lattice deforms. This deformation of the
lattice influences another electron, and an
electron-electron coupling results; each
electron with equal and opposite momenta.
These Cooper pairs condense into a single
macroscopic quantum-mechanical state
described by the wave BCS function
𝜓 = 𝑛 𝑠 𝑒 𝑖𝜑
.
This quantum state carries current without
dissipation, known as a supercurrent6
.
Figure 1 – Cartoon representation of the electronic transport
regimes for metallic contacts. The (elastic) inelastic mean
free path of the electrons is represented by (𝑙 𝑒𝑙)𝑙𝑖𝑛, the
contact size is d and is shown as the pink circles. The ballistic
regime is characterized by having no collisions inside the
contact area and in this case, we can detect spectroscopic
information. In the diffusive regime, there is elastic
scattering that takes place which gives weak spectroscopic
information. If a contact is in the thermal or Maxwell limit,
large amounts of scattering occurs in the junction area.
Energy is lost to joule heating and spectroscopic information
is smeared. Adapted from [5].
Thermal
𝑙𝑖𝑛 ≪ 𝑑
d
e-
𝒍
e-
e-
𝒍
e-
d
e-
𝒍
e-
Ballistic
𝑙 𝑒𝑙 ≫ 𝑑
Diffusive
𝑙 𝑒𝑙 < 𝑑 < √𝑙 𝑒𝑙 × 𝑙𝑖𝑛

3. The following experimental results were
initiated with the intention of applying well-
understood PCS procedures on
superconductors to quantum critical
materials in order to make advancements
toward providing evidence of the quantum
theory of PCS in correlated materials.
Through completion of this research and
verification of the quantum theory of PCS, a
filter for non-Fermi liquid behavior could be
developed.
Figure 2 depicts the orthorhombic crystal
structure of the quantum critical material
being used in this scientific investigation.
This material is YFe2Al10 and is thought to
be quantum critical based on quantum
critical scaling studies of susceptibility,
resistivity, and specific heat. The quantum
critical fluctuations are reported to exist in
the ac plane of the crystal7
.
Quantum criticality is a type of non-Fermi
liquid behavior. Quantum critical matter is at
or close to a quantum phase transition where
the material exists in an unstable state and the
conventional, or Fermi liquid properties of
the material can break down. A common
method of making a material quantum
critical has been to “tune” the properties of
the material through doping, pressure, or
magnetic fields. YFe2Al10 is intrinsically
located near a quantum critical point and
exhibits quantum critical behavior without
such tuning7,8,9
. Previous work on this
material shows a potential feature in the PCS
spectrum which could be associated with the
quantum critical behavior10
. A ballistic
contact is necessary to obtain relevant
spectroscopic information on the YFe2Al10.
Since no established quantum critical
behavior has been documented in the
ballistic limit, superconducting materials are
used as the counter-electrode to help
determine if the contacts are in or near this
limit. Once ballistic contacts are made and
are confirmed below Tc of the
superconductor, the temperature can be
raised to look for signatures of quantum
fluctuations above the Tc of the
superconductor. This research has begun the
investigation of quantum critical behavior
signatures in PCS spectra.
II. Methods
A. PCS Study of FeTe0.55Se0.45
A crystal of FeTe0.55Se0.45 was obtained from
through our collaboration with Dr. Genda
Gu’s group at Brookhaven National
Laboratory. To construct the soft PCS
junctions, the crystal is cleaved and an
aluminum oxide (Al2O3) insulating layer is
deposited using a Denton Vacuum DV-502A
chamber. 5 μm aluminum foil wires are
attached to the sample using Leitsilber 200
conductive silver paint. Two bottom
electrodes are connected directly to the
crystal. The point contacts are connected to
the Al2O3 layer and constructed by making v-
shaped wires acting as the two probes to the
counter electrode. This method makes use of
nanoscale channels that are introduced by
fritting2
through the Al2O3 barrier. The
micro-shorts, if in the ballistic limit, allow
Figure 2 – Left: Photograph of YFe2Al10 crystal with the
a and b axes labeled. The grid is 1 mm square. Right:
The crystal structure of YFe2Al10. Figure extracted from
[7].

4. 0 5 10 15 20 25 30 35 40
0
100
200
300
400
500
600
700
Resistivity(cm)
Temperature (K)
0 50 100 150 200 250 300
0
500
1000
FeTe0.55Se0.45
Resistivity(cm) Temperature (K)
for energy resolved spectroscopic
information. The sample is mounted to a
probe, the air is pumped out, and then
replaced with helium gas. The probe is then
lowered into a Dewar of liquid helium to
gradually cool the sample to ~ 4.2 K. A zero
bias conductance measurement is taken
during cool-down and warm-up using
LabView. Once cooled down, differential
conductance vs. bias measurements are taken
at varying temperatures.
B. Growth and PCS Study of Pb Thin Films
500 nm of lead followed by 22 nm of
aluminum is deposited onto a sapphire
substrate by thermal evaporation. The edges
of the lead layer are masked during the
deposition of the aluminum layer, and the
bottom electrodes are connected directly to
the lead. Three point contacts are attached to
the insulating layer and the same PCS
method as described in part A is used to
collect data.
C. PCS Study of YFe2Al10
A crystal of YFe2Al10 is polished to have a
flat surface and cleaned with an
acetone/methanol mixture for 5 minutes,
then with isopropanol for 5 minutes using
ultrasonic agitation. The clean crystal is
mounted onto a glass slide with the polished
side facing up. A 60 nm Pb layer followed by
a 22 nm Al2O3 is then evaporated onto the
flat surface of the crystal. The method
described in part A is used to collect data.
III. Results and Discussion
A. PCS Study of FeTe0.55Se0.45
The resistivity of the material is measured
from 300 K to 4.5 K (Fig. 3). This
measurement confirms the previously
established Tc of FeTe0.55Se0.45 to be 14.2
K11
. The value midway through the
resistivity drop is taken as Tc.
The crystal is then ready for PCS
measurements. The junctions are shown as
the center contact and the upper right contact
in Fig. 4. There was no insulating aluminum
oxide layer deposited. The junction
resistance was measured at 6 Ω.
Figure 3 – Top: dc electrical resistivity versus
temperature measurement on FeTe0.55Se0.45 from
300 K to 4.5 K. Bottom: Zoomed in resistivity
versus temperature around Tc, which is taken as
midway through the resistivity drop and
experimentally determined to be 14.2 K.
Figure 4 – Photograph of junctions
made on the FeTe0.55Se0.45 crystal for
ZBC and differential dI/dV
measurement.

5. A zero bias conductance (ZBC)
measurement (Fig. 5) was taken from 300 K
to 4.5 K. The ZBC curve is a measure of the
derivative of the conductivity as a function of
temperature without varying the bias. This
measurement gives insight into which
regime the junction is in. In the ZBC
measurement, joule heated junctions in the
thermal regime follow an inverse resistivity
function, since structural or magnetic
transition will be apparent, as opposed to
those in the ballistic limit3
.
The ZBC spectrum is clearly not the inverse
of the resistivity measurement, thus it is
possible that the contact is not in the thermal
regime. However, we do not expect such
variation in the ZBC with temperature, and
thus the contacts cannot be assumed to be in
the ballistic region either.
While at 4.6 K, a conductance measurement
with respect to varying bias was taken and is
displayed in Fig. 6B. The same measurement
was taken at subsequent temperatures shown
in the spectra in Fig. 6B.
The peak that is associated with Andreev
reflection disappears above Tc, further
confirming the junction is in the diffusive
limit.
The crystal was then cleaved and an 84 Å
Al2O3 insulating layer was deposited onto the
surface. The junction resistance was
measured at 75 ohms. The sample and
junctions are pictured in Fig. 7, where the PC
junctions are the top center contact and the
bottom right corner contact.
-40 -20 0 20 40
0.08
0.10
0.12
0.14
0.16
0.18
4.3 K
6.1 K
8.1 K
10.2 K
12.6 K
16.5 K
dI/dV(S)
Sample Bias (mV)
-40 -20 0 20 40
0.08
0.10
0.12
0.14
0.16
0.18
4.3 K
dI/dV(S)
Sample Bias (mV)
Figure 5 – The temperature dependence of the
differential conductance at zero bias (ZBC) from
300 K to 4.5 K.
Figure 6 – A: The temperature variation of dI/dV versus
bias shows that the superconducting peak disappears
after the temperature is raised above the Tc of
FeTe0.55Se0.45. B: The differential conductance (dI/dV)
plotted versus bias for 4.3 K.
Figure 7 – Junctions made on cleaved
FeTe0.55Se0.45 crystal.
0 50 100 150 200 250 300
0.00
0.05
0.10
0.15
0.20
0.25
FeTe0.55Se0.45
dI/dV(S)
Temperature (K)
ZBC

6. As can be seen in Figure 8, Andreev
reflection was observed and the measured
energy gap or ~20 meV, was estimated by
measuring the difference between one
maxima of the double peak and zero bias.
The top dI/dV versus bias spectra in Figure 8
has been normalized to account for slight
junction changes throughout the
measurement process. The double peak
reduced to a single peak as the temperature
was increased. Once the temperature was
increased to above Tc, this feature of the
superconductor disappears. By attaining the
spectra in Figure 8, the project continued to
the next stage.
B. Growth and PCS Study of Pb Thin Films
Since there is no established understanding
of the PCS signatures in quantum critical
materials, the challenge is to show this before
assuming that the dI/dV data is showing
spectroscopic information. A 500 nm thick
film of lead was grown with a 22 nm thick
Al2O3 insulating layer on top. The contact
used in the measurements is shown in Figure
9.
The ZBC curve shown in Figure 10 is
uncharacteristic of Pb due to the dip in the
conductance at ~200 K. A smooth linear
curve was expected. A superconducting
conductance jump at ~7 K confirms the Tc of
lead.
Figure 10 – The ZBC versus temperature
measurement has an uncharacteristic dip at ~200 K.
The superconducting jump at ~7 K confirms the Tc
of Pb.
Figure 9 – Photograph of the junction made
on a Pb thin film used to take ZBC and dI/dV
versus bias measurement.
4.8 K
6.1 K
8.2 K
12.4 K
14.2 K
16.4 K
-100 -50 0 50 100
10.5
11.0
11.5
12.0
12.5
13.0
13.5
normalizeddI/dV(mS)
Sample Bias (mV)
4.8 K
-100 -50 0 50 100
11.0
11.5
12.0
12.5
13.0
13.5
dI/dV(mS)
Sample Bias (mV)
Figure 8 – Bottom: dI/dV versus bias at 4.8 K shows
a superconducting peak and the desired Andreev
reflection. Top: The temperature variation of dI/dV
versus bias. As the temperature increased, the
spectroscopic information is less resolved.
0 50 100 150 200 250 300
0.10
0.12
0.14
0.16
0.18
dI/dV(1/)
T (K)
ZBC
Pb/AlOx 500nm/22nm

7. The uncharacteristic behavior continued into
the dI/dV measurements shown in Figure 11.
The Andreev reflection double peak
structure that was expected was seen,
however, with a different energy gap than
expected. The energy gap of Pb is ~2.1 meV
and the experimentally determined value was
6.9 meV, as shown via the red fit line on the
bottom graph of Figure 11.
The study of Pb gave an idea of how the
material would behave when deposited onto
the YFe2Al10. The process of making
contacts in the ballistic limit was practiced
and understood before moving onto the
YFe2Al10 crystals to study quantum critical
behavior in PCS.
C. PCS Study of YFe2Al10
A 60 nm layer of lead followed by a 22 nm
layer of Al2O3 was deposited onto a flat
surface of the YFe2Al10 crystal. The contacts
are shown in Figure 12, where the PC
junctions are the two top contacts and the
bottom middle contact. The measured
junction resistance was 6.8 ohms.
The ZBC measurement in Figure 13 is what
was expected of the pure Pb film. A
superconducting conductance jump at ~7 K
means that the Tc of lead was seen in the ZBC
spectrum.
The dI/dV spectra in Figure 14 confirm the
suspicions that only the Pb was being
measured. The spectra correlate to
0 50 100 150 200
0.04
0.06
0.08
0.10
0.12
0.14
0.16
ZBC
dI/dV(1/)
T (K)
Figure 12 – Photograph of the junctions
made on Pb/Al2O3/YFe2Al10 crystal for ZBC
and dI/dV versus bias measurements.
Figure 13 – The ZBC versus temperature
measurement shows a smooth curve with a
superconducting jump at ~7 K. This is what was
expected from the pure Pb sample.
Figure 11 – Bottom: The dI/dV versus bias shows
the desired Andreev Reflection. The red line is a fit
to BTK theory. Top: The superconducting features
disappear when the temperature was raised above Tc
of Pb.
-30 -20 -10 0 10 20 30
0.16
0.17
0.18
dI/dV(1/)
Sample Bias (mV)
4.6 K
5.2 K
6.6 K
7.0 K
7.8 K
9.7 K
13.4 K
22.6 K
33.6 K
Pb/AlOx 500nm/22nm
-30 -20 -10 0 10 20 30
0.16
0.17
0.18
AlOx/Pb T=4.6K
Z=0.417, G=7.25, d=6.9
dI/dV(S)
Bias (mV)

8. previously obtained PCS data on
superconducting materials.
It was determined that the YFe2Al10 crystal
was acting as a substrate and the quantum
critical behavior was not being seen in the
measurement because the current and
voltage loops were measuring through the Pb
film which means the scattering processes
were not happening in the YFe2Al10, but in
the Pb instead.
V. Future Work
The next procedure will involve trying to
make a tunnel junction as pictured in Figure
15. Similar to the original method of PCS12
the hope is to apply a high enough current
which will result in a leaky junction. If the
junctions successfully get shorted in this
method, spectroscopic information about
both the Pb and the YFe2Al10 can be obtained
by these “point contacts”.
The microshorts will develop through the
thin Al2O3 insulating layer. The idea is to see
the superconducting behavior of the Pb
below 7.2 K in order to see what regime the
contact is in. The quantum fluctuations will
be observed when the temperature is between
the lowest temperature and 30 K.
Theoretically, if the contact between the Pb
and the YFe2Al10 is ballistic, then the
quantum critical behavior as well as the
superconducting behavior should appear in
the spectrum.
The YFe2Al10 crystal has to be oriented so
that the ac plane of the crystal is being
-40 -30 -20 -10 0 10 20 30 40
0.115
0.120
0.125
0.130
0.135
0.140
0.145
0.150
dI/dV(1/)
Sample Bias (mV)
4.5 K
5.8 K
7.0 K
8.6 K
-30 -20 -10 0 10 20 30 40
0.12
0.13
0.14
dI/dV(1/)
Sample Bias (mV)
4.5 K
YFe2Al10
Thin Al2O3 layer
Thick insulating material
Deposited Pb strips
V
-
V+
I-
I+
V+ I+
I-V
Figure 14 – Bottom: dI/dV versus bias on the
YFe2Al10 sample. Top: Variation with
temperature of the differential conductance
versus bias.
Figure 15 – A leaky tunnel junction should allow the
Pb to be used as the point contact. The microshorts
will develop through the Al2O3 layer.

9. measured. Once oriented, the quantum
fluctuations will cause the desired behavior,
and the signature in the spectrum should
appear more frequently when in the ballistic
regime.
IV. Conclusions
Ballistic contacts were successfully made on
superconducting materials. This was
demonstrated by achieving good Andreev
reflection data in both FeTe0.55Se0.45 and Pb
samples. The intrinsic quantum critical
material, YFe2Al10, was used to begin the
study of correlated materials using PCS. A
method for determining the electronic
transport regime of the contact had to be
established. A preliminary attempt to
establish this method did not show quantum
critical behavior in the spectrum, but it
provided information on the current growth
scheme. Through explorations into quantum
critical behavior in PCS, a filter for non-
Fermi liquid behavior can be developed. This
development could subsequently be applied
to expand the possibilities in material science
research.
VI. Acknowledgments
I would like to thank Jennifer Misuraca,
Laura Greene, Wan Kyu Park, Ryan
Tapping, and Konrad Genser for their
guidance and help with this project. This
work is supported by the National Science
Foundation, Grant No. PHY-1062690.
*Permanent Address: Department of Physics -
The College at Brockport: SUNY;
aland4@u.brockport.edu
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