nernst effect as a probe of superconducting fluctuationsmsm09/behnia.pdf · nernst effect as a...
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![Page 1: Nernst effect as a probe of superconducting fluctuationsmsm09/behnia.pdf · Nernst effect as a probe of superconducting fluctuations Kamran Behnia Ecole Supérieure de Physique et](https://reader030.vdocuments.us/reader030/viewer/2022040113/5f0eecdb7e708231d4419d58/html5/thumbnails/1.jpg)
Nernst effect as a probe of
superconducting fluctuations
Kamran Behnia
Ecole Supérieure de Physique et de Chimie Industrielles
Paris
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• Luis Balicas, NHFML (Tallahassee, US)
• Ilya Sheikin & Arlei Antunes, GHMFL (Grenoble, FR)
• Baptiste Vignolle & Cyril Proust, LNCMP (Toulouse,FR)
• Yakov Kopelevich (Campinas, BR)
Samples
Claire Kikuchi, Laurent Bergé, Louis Demoulin (Orsay)
Jean-Paul Issi (Louvain-la-neuve)
Collaborators
ESPCI researchers:
Alexandre Pourret, Benoît Fauqué, Aritra Banerjee,
Zengwei Zhu, Huan Yang, Hervé Aubin
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OUTLINE
• Introduction
• Superconducting fluctuations• Nernst signal of short-lived Cooper pairs
• Quantum ocillations across the
quantum limit• Nernst profiles in graphite and graphene
• Fractional states in bulk bismuth?
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Thermoelectric coefficients
• In presence of a thermal gradient, electrons produce an electric field.
• Seebeck and Nernst effect refer to the longitudinal and the transverse components of this field.
JQ
T
xE
yE
B
TESx
x
T
ESeN
x
y
xyy
][
TB
E
xz
y
hotcold
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Set-up for monitoring thermal(kxx, kxy), thermo-electric (S, N) and electric (sxx, sxy) conductivity tensors
20 mm
Thermometers
Heater SC wires
9000 9060 9120 9180 9240 9300 9360 9420 9480 9540 9600 9660 9720
-52
-50
-48
-46
-44
-42
-40
-38
-36
dV
(n
V)
T(s)
DC voltages of the order of 1 nV resolved!
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Nernt response of normal electrons can be very large!
0.2 1 10 50
0.1
10
1000
NbSe2
CeRu2Si
2
CeCoIn5
URu2Si
2
PrFe4P
12
absolu
te v
alu
e)
(V
K-1T
-1)
T(K)
Bi
KB, M.A-Méasson & Y. Kopelevitch, PRL 2007
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Semi-classical picture
F
HBxy
e
TkS
22
3
TETJ
TEJ
Q
e
k
s
22
xyxx
xyxxxxxy
xySss
ss
If shifting the Fermi level does not change the Hall angle,then there is no Nernst signal!
xy
xxH
s
s
ss 10 STEJe
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Roughly, the Nernst coefficient tracks /EF
Bismuth URu2Si2 PrFe4P12
n (per f.u.) 10-5 3 10-2 2 10-3… and becomes large in
clean semi-metals!
~ 2/3 kB/e / EF
F
HBxy
e
TkS
22
3
KB, J. Phys.: Condens. Matter
21, 113101 (2009)
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Nernst effect and
superconcucting fluctuations
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Nernst effect in the vortex state
• Thermal force on the vortex :
F=-Sf T (Sf : vortex entropy)
• The vortex moves
• The movement leads to a transverse voltage: Ey=vx Bz
A superconducting vortex is:
• A quantum of magnetic flux
• An entropy reservoir
• A topological defect
B
Ey
T
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Vortex-like excitaions in the normal state of the underdoped cuprates?
A finite Nernst signal in a wide temperature range above Tc
Wang, Li & Ong, ‘06
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Nernst effect due to Gaussian fluctuations of the amplitude of the superconducting order parameter
(Usshishkin, Sondhi & Huse, 2002)
Quantum of thermo-electric conductance (21 nA/K)
In 2D:
In two dimensions, the coherence length is the unique parameter!Both the amplitude and the T-dependence of xy is determined by x(T).
Magnetic length
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Our main result!
1. This theory is experimentally verified!
2. In a conventional dirty 2D superconductor, a signal due to fluctuating superconductivity can be resolved by Nernst measurements at T>>Tc.
A. Pourret et al. Nature Phys. 2, 683 (2006); Phys. Rev. B. 76, 214504 (2007)
For a review see New J. Phys. , 11, 055071 (2009)
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Superconductivity in Nb0.15Si 0.85 thin films
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00
300
600
900
1200
1500
d=1000 A
d=500 A
d=250 A
d=125 A
T(K)
Rsquare(
)
The normal state is a simple dirty metal: le~a~ 1/kF !
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A Nernst signal persists deep into the normal state!
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A signal distinct from the vortex signal
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The link between and xy
In our case:
sxx > 103 sxy
sSC < 10-1 sxx when T > 1.1 Tc
Therefore: xy/ B = sxx= / Rsquare
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Link to the superconducting coherence length
yields
cB
Fd
Tk
v
2
336.0
1
x
This should be compared to the expression for a 2D dirty superconductor:
T-dependence= (T-Tc/Tc)
Amplitude
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The shortest link between data and vFle
1251035.4 smvF
e
B
e
Fe
k
Tv
s
k2
3
Using specific heat and resistivity data, this yields:
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Coherence length above Tc
0.1 1 102
10
60
x=
(5
.9 1
0-7
x
y/B
)1/2
(nm
)
= (T-Tc)/T
c
sample 2
sample 1
Satisfactory agreement for small !
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The ghost critical field
Contour plot of N= -Ey /(dT/dx)
Sample 2
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A unique correlation length
cB
Fd
Tk
v
2
336.0
1
x
Contour plot of N/B
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Why does it work so well here?The Nernst signal of the normal electrons is negligible in this dirty superconductor!
In Nb0.15 Si0.85 mobility is small and Fermi energy is large!
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Qunatum oscillations in
Nernst response
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Quantum oscillations of thermoelelctric coefficients in Bi
KB, M.A-Méasson & Y. Kopelevitch, PRL 2007
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Giant quantum oscillations
0.0 0.3 0.6 0.9
0.1
1
10
31
02
1
2
1
0
3 1.20 K
0.46 K
0.28 K
B-1 (T
-1)
Sxy(m
V/K
)1-
2-
3-
0+
1+
unidentified
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Quantum oscillations in graphiteZhu et al., Nature Physics, Nov. 8 2009
1 105
10
80HOPG sample 2
Sxy (V
K-1)
B(T)
1.65 K
0.98K
0.77 K
0.55 K
0.34 K
0.29 K
40
100
1000
40001 10
4.2 K
HOPG sample 1
1.6 K
2.7 K
8 K
16 K
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Quantum oscillations in Graphene
See also:
Wei et al., PRL’09
Checkelsky and Ong, arXiv: 0812.2866
When a Landau level meets the
Fermi level, Sxy vanishes!
Zuev, Chang & Kim, PRL’09
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Theory for 2DEG
Oji, J. Phys. C ‘84
Jonson & Girvin, PRB ‘84
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Empirical correlation between the Nernst profile and dimensionality!
3D
0.00 0.15 0.30 0.45 0.60 0.75 0.90 1.05
100
1000
Ne
rnst S
ign
al V
y (
nV
)
B-1 (T
-1)
nV, 312mK
nV, 475mk
nV, 760mK
nV, 910mK
0.00 0.15 0.30 0.45 0.60 0.75 0.90
10
100
0.343K
0.549K
0.678K
0.771K
0.805K
0.853K
0.976K
1.651K
Sxy (V
/K)
B-1(T
-1)
2D
bismuth
graphite
GaAs
graphene
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A topological phase transition in 3D
For a review paper on topological
phase transitions, see:Blanter, Kaganov, Pantsulaya and
Varlamov
Phys. Rep. 245, 159 (1994).
Zhu et al., Nature Physics 09
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What happens beyond the quantum limit?
The quantum limit (9T)
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Peaks beyond the quantum limit
KB, L. Balicas & Y. Kopelevich, Science 2007
•Do not correspond to any obvious integer Landau
level
•Are not periodic in 1/B
•Are concomittant with Hall anomalies
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Length scales and Nernst coefficient in Bi
Bismuth
T=1.5 K
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A surprise at still higher fields!No more Landau level
crossing is expected!Fauqué et al. New J. Phys. 11 113012 (2009)
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All these states are expected to deteriorate metallicity!
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The hig-field anomaly looks like a LL crossing!
The T-dependence confirms a hole-ellipsoid origin!
No critical temperature!
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Topological and symmetry-breaking phase transitions (Xiao-Gang Wen, Adv. Phys. 1995)
symmetry - breaking topological
•The ground state is a quantum crystal
•An order parameter
•A critical temperature
•The ground state is a quantum liquid
•No order parameter
•No critical temperature
Examples: SC, DW,… Examples: QHE (Integer and fractional)
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Summary
Nernst effect is a sensitve probe of :
• superconducting fluctuations
• quantum oscillations
• 3D metal beyond the quantum limit
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Electron spectrum in bismuth at high field
When the field is along trigonal and exceeding 11 T
Holes at their lowest LL; electrons at their lowest Zeeman-splitted LL!
But, is this true?
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Electron spectrum in bismuth at high field
Sharlai
&
Mikitik
PRB
2009
The magnetic field displaces the Fermi Energy, in
order to preserve charge neutrality: nh=ne1+ne2+ne3
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A very anisotropic field scale associated with electron pockets
Lu Li et al., Science 08
Alicea & Balents PRB 09
ExperimentSharalai &
Mikitik, PRB 09
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Are the high-field Nernst peaks a result of small
misalignment?
• In case of perfect alignment, no anomaly beyond 10T is expected!
Sharalai & Mikitik, PRB 09
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Are the high-field Nernst peaks a result of small
misalignment?
• But there is an arbitrary angle for which three high-field e- anomalies are expected!
Sharalai & Mikitik, PRB 09
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Angular dependent Nernst effectH. Yang et al., unpublished
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Angular dependent Nernst effect
ANGLE (DEGREES)
Fie
ld (
Tesla
s)
B. Fauqué, LNCMI-Grenoble
3 AM 10 /09/09
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Angular dependent Nernst effect
Quasi- horizontal lines and quasi-vertical lines
0+e
1-e
?
?
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When the field is aligned along trigonal
The temperature dependence confirms an e- ellipsoid origin!
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HOPG and natural graphite
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Thermopower and Nernst effect in graphite
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Non-trivial Berry phase in graphite