Nernst signal in low-Tc disordered
superconductors
Alexandre Pourret
INAC/ SPSMS/ IMAPEC
CEA Grenoble
Collaborators
• Kamran Behnia
• Hervé Aubin
• Panayotis
Spathis
• Jérôme Lesueur
ESPCI
Paris
Samples
 C. Kikuchi, L.Bergé, L. Demoulin (CSNSM Université
Paris Sud 11, France)
 Z. Ovadyahu (Racah Institute of Physis Tel Aviv, Israel)
Outline
I.
Nernst effect and experimental setup
Thermoelectrics coefficients
Nernst effect
Experimental setup
II. Superconducting fluctuations in NbxSi1-x
Observation of a non-zero Nernst signal aboveTc
Origin of the Nernst signal above Tc
Comparison with the theoritical prediction
III. The InOx case
Comparison with NbxSi1-x
Thermoelectric coefficients

E
x
S
xT
Thermoelectric power

E
y
N
xT


Ex

B
JQ
Nernst signal
 Ey
Bz  xT

Ey
Nernst coefficient

 Je
 
J
 Q

T
  

 
  T

  E
 


 
  T
1  xy xx   xx xy

B  xx2   xy2




Sondheimer cancellation (1948)
Counterflow of hot and cold electrons
e-
eB
e-
e-
e-
eJQ≠0;Je=0;Ey=0
e-
eHot side
Cold side
T
In an ideally simple metal, the Nernst effect vanishes!
Roughly, the Nernst coefficient tracks m/ eF…

 2 k B2  H

T
3 e e

eF
 2 k B2 m
 
T
3 e eF
Boltzmann equation
mobility
Low Fermi Energy = high Nernst signal!
e
m
m*
Recipe for a large diffusive Nernst response:
•High mobility
•Small Fermi energy
•Ambipolarity

 2 k B2 m

T
3 e eF
Nernst signal generated by moving vortices
Fα-Sf T
Vortices displaced by heat flow induce
a transverse electrical field
– the Nernst signal
Ri. H.-C et al
Phys. Rev. B 50, 3312–3329 (1994)
Vortex-like excitations in the normal state of the
underdoped cuprates?
Wang, Li & Ong, ‘06
A finite Nernst signal in a wide temperature range above Tc
Why measuring the Nernst signal of disordered
superconductors ?
Nernst effect is a very important probe since the discovery of a
large Nernst signal in the underdoped region of the cuprates.
Need to test theories of Nernst signal generated by
superconducting fluctuations in systems simpler than the
cuprates.
Interesting fluctuations phenomena




Kosterlitz-Thouless like transitions
Quantum superconductor-insulator transitions
Bose insulators
Bose metals
Experimental setup 1 heater -2 thermometers
Manganin Wires
Seebeck (S), Nernst (N), Hall angle
(RH) thermal conductivity  and
electrical conductivity .
Heater
Sample
Silver/Gold wire
-36
-38
4mm
-40
Cooper block
Ø 1.5 cm
dV (nV)
-42
-44
-46
-48
-50
-52
9000 9060 9120 9180 9240 9300 9360 9420 9480 9540 9600 9660 9720
T(s)
Thermometers
NbxSi1-x : an homogenous amorphous superconductor
Co-evaporation of Nb and Si.
1200
No granularity observed by AFM
800
R(W)
r=2 mWcm
Two samples 12.5 nm and 35 nm
Nb0.15Si0.85
d12.5 nm
Tc=220 mK
r mWcm
400
sample
Quartz Nb
Quartz Si
Ecran
0
0
50
100
150
T(K)
200
250
300
le~ a ~kF-1~ 0.7 nm
kF le ~1
Close to Mott-Ioffe
limit
RH  4.9  1011 m 3 / C
Si
Nb
carrier density is
large (1023 /cm3)
Superconductivity in Nb0.15Si
0.85
thin films
1500
d=125 A
Rsquare(W)
1200
900
d=250 A
600
d=500 A
300
d=1000 A
0
0.0
0.5
1.0
1.5
2.0
T(K)
T(K)
2.5
3.0
3.5
4.0
Above Tc, Cooper pairs fluctuations
Paraconductivity
1320
T=1.2K
Rsquare(W)
1300
Nernst effect can detect
Cooper pairs fluctuations
up to 30 * Tc.
1280
Tc=250mK
1260
0
1
2
T(K)
3
4
Theory : Fluctuations described in Gaussian approximation
-Aslamazov – Larkin; Physics Letters, 26 A, 238 (1968)
-Maki-Thomson
-Density of States
Magnetic field induced Quantum SuperconductorInsulator transition (Field perpendicular to sample plane)
1400
1300
Rsquare(W)
Rsquare(W)
1375
z~0.7
1350
1325
300mK
110mK
1200
1300
2
3
4
5
6
7
8
9
10
H(kOe)
0,0
0,5
T(K)
1,0
1,5
T
dR/dT < 0
Localized Cooper pairs ?
Finite size scaling
dR/dT > 0
Paraconductivity
T
c
H. Aubin et al. PRB 73, 094521 (2006)
Nernst signal above Tc (d=12.5 nm ,Tc=165mK)
in sample 1
A. Pourret et al.Nature Physics 2, 683 (2006)
0.4
0.4
0.2
0.4
190mK
B=2T
230MK
1500
mH=2T
310mK
Tc=0.165
K
370mK
460Mk
1000
530mK=0 T
500
00.0
0.1
0.2
0.2
0.0
0
0.0
1
1 0
0.19 K
0.19 K
)
 0  19nm
0.4
00.0
0.5
0.1
0.6
0.2
0.7
0.3
0.4
0.5
0.02
0.02
0.6 0.7
T(K)
(T)
2 
1 23 2
0.19 K
0.04
0.04
500
T(K)
(T)
0.06
Tc=0.165 K
(T)
0.00
4 3 0.00040
0.66K
0.85K
1.1K
1.38K
2.00K
0.66K
0.85K
1.1K 2.5K
0.66K
3.90K
5.40K
5.8K
1.38K
2.00K
2.5K0.85K
3.90K
0.06
=0 T
0.3
0.08
N (µV/K)
530mK
0.08
N
N(µV/K)
(µV/K)
0.6
N (µV/K)
N
N (µV/K)
(µV/K)
0.6
0.08
R_square(W)
0.8
R_carre(W)
190mK
230MK
190mK0.81500
310mK
230mK
310mK
370mK
370mK
460Mk
460mK0.61000
530mK
5.40K1.38K 5.8K2.00K
3.90K
5.40K
1.1K
2.5K
5.8K
0.06
0.04
0.02
0.001
01
(T)
32 3
(T)
(T)
212
Finite Nernst signal up to T=30*Tc and
B>Bc2 (0.85T)
43 4
4
Tc=0.165 K
1000
0.06
Nernst coefficient in sample 1 (Tc =165mK)
=0 T
500
00.0
0.2
0.0
N (µV/K)
0.4
370mK
460Mk
530mK
R_square(W)
N (µV/K)
0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.7
T(K)
0
1
2
(T)
3
4
0.04
0.02
0.00
0
1
2
(T)
3
4
 (µV/KT)
0.19 K
1
Sample 1
 is independent of
magnetic field at low
magnetic field
0.1
0.01
5.8 K
0.003
0.02
0.1
(T)
1
4
Nernst signal below and above Tc
(Sample 2, TC =380mK)
A signal distinct from the vortex signal
6
T>Tc
T<Tc
N (mV/K)
0.06
180mK
200mK
240MK
250mK
270mK
315mK
330mK
360mK
400mK
4
2
0.56K
0.65K
0.72K
0.85K
1.2K
1.6K
1.9K
2.5K
3.2K
4.3K
0.05
0.04
0.03
0.02
0.01
0
0.0
0.4
0.8
B (T)
1.2
0.00
0
1
2
B (T)
3
4
Two characteristic fields that evolve symmetrically with
respect to critical temperature
mV/K
Landau quantization of
the fluctuating Cooper pair motion
f0
B f
2
H 
2 2d
*
*
0
2
Below Tc : Bc2
Above Tc : B*
Normal state Nernst signal is very weak
n < S tan,
 Hall angle
The Cooper pairs life time is
larger than the quasi
particles life time :
GL= qp ( /le) 2
Why a dirty superconductor?
Compare the Ginzburg-Landau time scale and the quasi-particle lifetime:
GL= qp ( /le)
2
dirty(dirty)
qp
 2 k B2  QP

T
3 m* eF
dirtier
GL
GL> qp
n
0.2
1
e (T-Tc/Tc)
10
In a wide temperature range above Tc, Cooper pairs live much longer than quasiparticles and dominate the Nernst response!
What generates the Nernst signal above Tc ?
•The temperature dependence of maximum in the Nernst signal is controlled
by the superconducting correlation length
•We checked that the normal electrons do not have any contributions
•There is no reason to believe that exist, above Tc, a regime controlled by
phase fluctuations only.
Coopers pairs fluctuations, described by
theories in the Gaussian approximation,
should explain the data.
Theory: fluctuations of the super conducting order
parameter in Gaussian approximation
(I. Ussishkin et al. Phys. Rev. Lett. 89, 287001 (2002))
At 2D
At low magnetic field
Close to Tc

1 kBe d

2
6   B
2
SC
xy

xx > 103 xy et SC < 10-1 xx
Rsquare

Quantum of thermoelectric
conductivity
(21 nA/K)
SC
 XY
B
BCS correlation length :
3 v F 
d 
0.36
2 k BTc
e
1
With v   4.35105 m2 s 1
F
Marnieros (2000)
Precise prediction
Reduced temperature:
 xy
B
USH
T
)
Tc
e  ln(
 k Be 2  2
.ξ
 
2  d
 6π 
Comparaison with the theoretical prediction
SC
 XY
xy/B(mA/TK)
0.01
is independent of
the magnetic field at low field.
B
1E-3
1E-4
1E-5
0.02
xy/B(mA/TK)
T=410mK
T=450mK
T=560mK
T=640mK
T=820mK
T=1.6K
T=3.2K
Sample 2
Tc=380 mK
0.1
B (T)
1
4
0.01
The amplitude of signal is
consistent with theory , close
to Tc (B->0), with no
adjustable parameters.
1E-3
1E-4
xy/B (Sample2) (B=0)
1E-5
xy/B (USH)
0.02
xy/B (Sample1) (B=0)
0.1
1
-2
eln(T/TC) d
4
The Nernst signal is determined only by the size of
superconducting fluctuations
mV/KT
mV/KT
lB
lB
A. Pourret et al. PRB 76, 214504 (2007).
 (nm)
 (nm)
d
d
Pour B>B*, the caracteristic length is lB 
Pour B<B*, the caracteristic length is d
f0
2B
A. Pourret et al. PRB 76, 214504 (2007).
Nernst signal is sensible to 
= lB
f0
B 
2
2d
*
d = l B
d
generalized correlation length
The magnitude of the Nernst coefficient at high magnetic
field can be predicted
d (nm)
The same function F()
determine xy/B:
xy/B(mA/TK)
50
With d for B <
F(d)
xy/B (USH)
1E-3
d2
B=0
d4
1E-5
0.02
0.1
xy/B(mA/TK)
-21
50
l (nm)
B
F(0.93*lB)
xy/B (USH)(450mK)
1E-3
1E-4
1E-5
Landau quantization of
the fluctuating Cooper pair motion
10
T=450mK
F(lB)
0.01
= lB for B > B*
4
eln(T/TC) d
100
And
6.2
xy/B (B=0)
0.01
1E-4
B*
10
0.02
d(450mK)
0.1
-2
B(T) lB
1
4
At Tc, Nernst coefficient is determined by lB on the
whole magnetic field range, because d diverge
BSI
BC2
xy/B(mA/TK)
1
T=200mK
T=250mK
T=310mK
T=360mK
T=450mK
T=560mK
T=640mK
T=820mK
T=1.6K
T=2K
T=3.2K
F(lB)
0.1
0.01
1E-3
1E-4
1E-5
0.02
0.1
1
B (T)
F (lB) corresponds to
 xy
B
(Tc , B )
4
Other theoretical approaches
M. Serbyn et al. Phys. Rev. Lett. 102, 067001 (2009)
Kubo formulism
K. Michaeli, A. Finkelstein. Phys. Rev.B 80,
214516 (2009)
Quantum kinetic approach
One difference with cuprates
The case of InOx
M. A. Paalanen et al. Phys. Rev.Lett. 69,
1604 (1992).
V. F. Gantmakher et al. JETP Lett. 61, 606
80
T=0.32 K
(1995).
G. Sambandamurthy et al. Phys. Rev. Lett.
60
92, 107005 (2004).
R (kW)
V. F. Gantmakher, et al. JETP Lett. 71, 160
(2000).
10
R• (kW)
B=5 T
0.62 K
SIT
20
5
B=0 T
0
0

0.42 K
40
0
1
2
3
T(K)
4
Low carrier density: n=1021 cm-3
Weak phase stiffness
(Emery and Kivelson)
Ovadyahu Z.
5
Superconductor
1.20 K
2.10 K
0
3
B (T)
Bose Insulator
6
9
Metal
Nb0.15Si0.85
InOx
The coherence length doesn’t diverge
The case of InOx
Carrier density is 80 times
lower than Nb0.15Si0.85
Strong phase fluctuations
• No visible anomaly in
xy(T)!
• The vortex signal and the
fluctuation signal cannot be
distinguished!
Summary
A Nernst signal generated by fluctuating Cooper pairs (as
opposed to mobile vortices) can be resolved at T~30Tc in a
dirty superconducting film!
The magnitude of the signal is in very good agreement with
the theory.
The field dependence of this signal detects the “ghost
critical field”, confirming a superconducting origin.