Andreev reflection at the CeCoIn5 Heavy Fermion Superconductor Interface

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Andreev reflection at the CeCoIn5 Heavy Fermion
Superconductor Interface
Wan Kyu Park and Laura H. Greene UIUC John L.
Sarrao and Joe D. Thompson LANL Theoretical
support Justin E. Elenewski UIUC, Greene
group Vladimir Lukic UIUC, Leggett
group Anthony J. Leggett UIUC David Pines LANL
UIUC Experimental support Karen
Parkinson UIUC, Undergraduate Thesis
Student Caitlin Jo Ramsey UIUC,
Undergraduate B. Florian Wilken UIUC, German
exchange student, 03-04 Alex N. Thaler UIUC, REU
2003 Patrick J. Hentges UIUC, PhD, 2004, now at
Intel William L. Feldman UIUC, Lab Tech, retired
2003
Funding support US DoE, DEFG02-91ER45439
through FSMRL and CMM
RTS Workshop, June 10-11, 2005, Notre Dame, IN
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• Conditions 10ms after Big Bang
• 10 GeV/fm3 or 1016gm/cm3
• T 170 MeV or 2 x 1012 K
• Same physics as superconductivity,
  (strongly-correlated electron systems) but
  1016 different in energy !

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Outline

• Definition of Issues
• Andreev reflection between a heavy-fermion
  superconductor (HFS) and a normal (N) metal
• Point Contact Spectroscopy (PCS)
• The HF superconductor CeCoIn5
• Some Basics of Andreev Reflection and PCS
• Experiment Cantilever-Andreev-Tunneling (CAT)
• Data Analysis (extended BTK model)
• Known theories cannot explain AR at the N/HFS
  interface
• Some analysis consistent with d-wave and
  strong-coupling
• New data on (110) may show spectroscopic evidence
  for d-wave
• Conclusions

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Definition of the issues
1. Understanding charge transport across HF
interface Existing models cannot account
for Andreev reflection at the HFS/N
interface 2. Spectroscopic studies of CeCoIn5
(OP symmetry, mechanism, etc.,)
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The Heavy-Fermion Superconductor CeCoIn5
C. Petrovic et al., J. Phys. Condens. Matter 13,
L337 (2001)
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• Tc 2.3K (record high for HFS)
• ?0ab 82Å, ?0c 53Å, ?ab 1900Å, ?c
  2700Å, Hc2ab(0) 12T, Hc2c(0) 5T
• Superconductivity in clean limit (l gtgt ?0, l
  810Å)
• Non-Fermi liquid ? T 1.0 0.1, Cen / T
  -lnT, 1 / T1T T 3/4
• Heavy-fermion liquid
• - ?n Cen / T 0.35J/mol K2, ? meff 83m0
  heavy-fermion
• - ?(0) 10 -2 emu/mol
• - (? - ?0) / T 2 0.1??cm/K2 (under high
  pressure)
• - Transition from Kondo impurity fluid to
  coherent heavy electron fluid at T
• TK 1.7K (single ion Kondo temperature)
• T 45K (intersite coupling energy of Kondo
  lattice)
• CEF splitting120K (Nakatsuji, Pines, Fisk,
  PRL 92, 016401 (2004))
• Anisotropic type-II superconductor
• d-wave pairing symmetry? (Spectroscopic
  evidence is still lacking)
• FFLO phase transition? - Power-law
  dependence Cen / T T, ? T 3.37, 1/T1 T
  3?, ? T 1.5

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Layered-tetragonal Crystal Structure
Ce
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ANDREEV REFLECTION (no insulator) Normal
Metal/Superconductor (N/S)
In N Electrons retro-reflected as holes
e?
In S Cooper Pairs Broken near interface
h
N S
Probability of finding Cooper Pairs
Pair Breaking
N S
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Energy Scales for Andreev Reflection
E
EF (few V)
N
S
k
Particle conversion process that conserves
charge, energy and momentum!
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Probabilities
Blonder-Tinkham-Klapwijk (BTK) Model for charge
transport across the N/S interface PRB 25, 4515
(1982) Assumes (among other things)
Ballistic transport
A Andreev reflection B Normal reflection C
Transmission without branch- crossing
(electron-like) D Transmission with branch-
crossing (hole-like) A(E)B(E)C(E)D(E)1
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s-wave BTK Conductance

• Describes transitional behavior from AR to
  tunneling
• Effective barrier strength

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Extended BTK theory
S. Kashiwaya et al., PRB 53, 2667 (1996)
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d-wave BTK Conductance
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BTK model has worked well for a wide range of
materials, but NOT for HFS/N interfaces
The Fermi velocity mismatch is so great at the
HFS/N interface that Andreev reflection (AR)
should never occur (Zgt5, extreme tunneling
limit).
Recall the effective barrier strength
However, AR is routinely measured at the N/HFS
interface (many reports), albeit suppressed.
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Our Experiment Cantilever-Andreev-Tunneling
(CAT) rig
Gold tip - sharpened by electrochemical
etching CeCoIn5 single crystal - c-axis
oriented - etch-cleaned using H3PO4 Coarse
approach - done before inserting probe Fine
approach - done during cool down - piezo
driven by computer control Operation range -
Temperature down to 300mK - Magnetic Field
up to 12T
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Basics of PCS Contact Regimes
Length scales 2a contact size lel elastic mean
free path lin inelastic mean free
path x coherence length
For our experiment Upper limit of 2a 46
nm lel at Tc is 81 nm (from thermal
conductivity), and increases with decreasing
T, to 4-5 µm at 400mK.
Therefore, our experiments are in the ballistic,
Sharvin Limit, required for good spectroscopy
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DATA Dynamic Conductance of Au/CeCoIn5
Background develops an asymmetry at the
heavy-fermion liquid coherence temperature, T
45 K, gradually increasing with decreasing
temperature to the onset of superconducting
coherence, Tc 2.3 K.
T
Tc
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Background Normalization
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s-wave fit
G(T)?(T)
BUT Decreasing ? with decreasing T Not
physically meaningful
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d-wave fit
BUT AGAIN, decreasing ? with decreasing T (like
s-wave case) So again, Not physically meaningful
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Zero-bias Conductance Fit (one point)
Constant G Supportive of d-wave pairing
symmetry, consistent with literature
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Similar AR magnitudes Common in N/HFS
URu2Si2-Pt
Yu. G. Naidyukv et al., Europhys Lett. 33, 557
(95).
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VERY NEW DATA PCS on 110-orientation
Spectroscopic proof of d-wave ??? (work in
progress)
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Temperature Dependence Can normalize as the
c-axis data
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Note magnitude of Andreev signal is the SAME as
for the (001) PCS! This supportsA) Intrinsic
property (reproducibility indicates not a
barrier effect)B) Sharvin limit
Shape supports d-wave May be 1st spectroscopic
evidence.
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BTK Conductance s-wave vs. d-wavework in
progress
s-wave
d-wave ab-plane
d-wave c-axis
a ?/4
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Models which address the observation of AR at
HFS/N Interface
1. Deutscher and Nozières, PRB 50, 13577 (1994)
From PCS of N/HFS, it has been common to obtain
conductance curves corresponding to low Zeff
value. Deutscher and Nozières argument The
boundary condition at the interface involves
Fermi velocities without mass-enhancement
factors.
2. N. A. Mortensen et al., PRB 59, 10176 (2000)
Mismatch of Fermi Momenta combined with the
two-fluid model of Nakatsuji, Pines Fisk causes
strong effect on tunneling cone. Zeff must be
calculated for each component. This effect can
explain ZBC normalized to normal state
conductance, but not to high-bias conductance.
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Breakdown of the Andreev Approximation
3. A. Golubov and F. Tafuri, PRB 62, 15200
(2000)

• Retro-reflection whenever D ltlt EF (Andreev
  approximation).
• If D/EF is non-negligible, the hole does not
  trace back the electron trajectory exactly
  (breakdown of Andreev approx.).

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Energy-Dependent QP Lifetime
4. F. B. Anders and K. Gloos, Physica B 230-232
437 (1997)

• Causes a reduction in gap energy
  (renormalization due to the strongly reduced QP
  spectral weight)
• Causes asymmetry with the emergence of coherent
  heavy quasi-particles

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Conclusions

1. Clean dynamic conductance data are measured
   between 60 K and 400 mK across HFS/N (CeCoIn5/Au)
   nano-scale junctions
2. Careful investigations show the contact is in the
   Sharvin limit.
3. Existing models cannot adequately describe the
   particle-hole Andreev conversion process at the
   HFS/N interface.
4. The low-temperature (400mK) conductance curve is
   consistent with strong coupling and the
   temperature-dependence of a single point, the
   zero-bias conductance, is consistent with a
   d-wave order parameter symmetry, both conclusions
   consistent with the literature for CeCoIn5.
5. We propose that systematic corrections to the BTK
   model that go beyond the breakdown of the Andreev
   approximation and re-normalized Fermi momenta may
   provide a framework for our future understanding
   of Andreev reflection at the N/HFS interface.
6. Recent (110) data may be spectroscopic evidence
   for d-wave

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Biscuits
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Is the Contact in Sharvin Limit?

• Contact Size, d O 500 Å using Wexlers formula
  with RNR0(1Z2), RN 1 ?, Z 0.35, ?Tc 3.1
  ??cm
• ?0 82Å
• lel 4-5 mm, lin 0.65 mm _at_400mK
• ?0 lt d ltlt lel, lin
  ? Contact is ballistic, even if considering
  reduced l in point contact

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How can we explain the background conductance?
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Heating Effect?

• Local minima not intrinsic but caused due to
  incomplete match of BC
• No minima in un-normalized data
• No heating effect due to non-ballistic contact ?
  Sharvin contact!

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Non-Ballistic Point Contact

• K. Gloos et al., JLTP 105, 37 (1996)
• dR dRA dRMAX
• In N/HFS point contact, Maxwell resistance
  dominates since the resistivity of HFS is large.

CeCoIn5 has relatively small resistivity ( 3.1
??cm) and extremely long electron mean free path
at low temperatures.? Sharvin(ballistic) point
contact could be formed
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The Four Questions

• Is the contact ballistic, diffusive, or
  thermal? (A Ballistic we have shown the
  Sharvin Limit)
• How can we explain the background conductance
  shape?? We observe a change in asymmetry at T
  
• What is the Pairing symmetry? (s-wave or
  d-wave)? fit the data using extended BTK models
• Why is the enhancement of sub-gap conductance so
  small? (13.3 _at_ 400mK, NOT 100 as in
  conventional SCs)? explore various
  possibilities

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Models to account for observaion of AR at HFS/N
Interface
Deutscher and Nozières, PRB 50, 13577 (1994)
From PCS of N/HFS, it has been common to obtain
conductance curves corresponding to low Zeff
value. Deutscher and Nozières argument The
boundary condition at the interface involves
Fermi velocities without mass-enhancement
factors.
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Quantum Critical Point Phase Diagram
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Calculated Resistance of Point-Contact
PCS in Sharvin limit - contact resistance
independent of materials resistivities - in
practical situation, heterogeneous contact
? x lt d lt l1, l2
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Is the Contact in Sharvin Limit?

• Contact Size, d O 500 Å using Wexlers formula
  with RNR0(1Z2), RN 1 ?, Z 0.35, ?Tc 3.1
  ??cm
• ?0 82Å
• lel 4-5 mm, lin 0.65 mm _at_400mK
• ?0 lt d ltlt lel, lin
  ? Contact is ballistic, even if considering
  reduced l in point contact

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Andreev Reflection
A. F. Andreev, Sov. Phys. JETP 19, 1228 (1964)
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Bogoliubov-de Gennes Equations
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Suggestions For Theoretical Study

• Successful model should explain the following
  experimental features.
• Concomitance of asymmetry in background
  conductance with emergent heavy-fermion
  liquid
• Suppressed Andreev reflection to quantify the
  full conductance curve
• Possible shrinking(?) of the conductance curve

• The following issues need to be investigated
  carefully.
• Mismatch in Fermi parameters effective mass,
  momentum, velocity
• Anisotropy order parameter, layered structure,
  Fermi surface
• Emergent heavy quasiparticles, two fluid model
• Quasiparticle scattering rate in AR process
  across N/HFS interface
• Length scales for electrostatic potential, order
  parameter, effective mass, etc., in terms of
  coherence lengths both in a normal metal and in a
  superconductor

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Mismatch of Fermi Momenta
N. A. Mortensen et al., PRB 59, 10176 (2000)

• This effect can explain the suppression of ZBC
  normalized to normal state conductance, but not
  to high-bias conductance.
• If the superconductor is inhomogeneous as in the
  two-fluid model (Nakatsuji, Pines Fisk), we can
  define different Zeff for each component. Were
  exploring this possibility.

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Breakdown of Andreev Approximation
A. Golubov and F. Tafuri, PRB 62, 15200 (2000)

• Retroreflection whenever D ltlt EF (Andreev
  approximation).
• If D/EF is non-negligible, the hole does not
  trace back the electron trajectory exactly
  (breakdown of Andreev approx.).
• This happens in layered structures, too.

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d-wave BTK Conductance
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MgB2 PCS
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