Nernst effect as a probe of Nernst effect as a probe of electronic correlations Kamran Behnia Ecole Supérieure de Physique et de Chimie Industrielles Paris
The team in ESPCI •Romain Bel •Alexandre Pourret •Hervé Aubin •Marie-Aude Méasson •Benoît Fauqué •Aritra Banerjee In collaboration with: • Luis Balicas, NHFML (Tallahassee) • Ilya Sheikin, GHMFL (Grenoble) • Yakov Kopelevich (Campinas , Brazil) p ( p , ) • Julien Levallois, Baptiste Vignolle & Cyril Proust, LNCMP (Toulouse) • Koichi Izawa & Jacques Flouquet, CEA (Grenoble) • Claie kikuchi & Louis Demoulin (Orsay) Claie kikuchi & Louis Demoulin (Orsay)
Outline Outline • On the magnitude of the Nernst effect in the zero- g temperature limit • Nernst effect as a probe of superconducting fluctuations (the case of Nb 0.15 Si 0.85 ) • Nernst effect and quantum criticality (the case of CeCoIn 5 ) • Nernst effect in the vicinity of quantum limit (the case of bismuth)
Thermoelectric coefficients Thermoelectric coefficients • In presence of a thermal gradient, electrons produce an electric field. r E r x • Seebeck and Nernst effect refer to the B longitudinal and the transverse components of this field. components of this field. hot r cold ld J Q E y r ∇ T − E − E y − E = = y y x x S S ν ν = = = = = [ [ ] ] N N e e S S ∇ T z ∇ y xy B T ∇ x T x x
Set-up for monitoring thermal( κ xx , κ xy ), thermo-electric (S, N) and electric ( σ and electric ( σ xx , σ xy ) conductivity tensors σ ) conductivity tensors Thermometers SC wires Heater -36 -38 -40 -42 dV (nV) -44 -46 -48 48 -50 -52 9000 9060 9120 9180 9240 9300 9360 9420 9480 9540 9600 9660 9720 T(s) 20 mm DC voltages of the order of 1 nV resolved!
Nernst effect in a single-band metal Absence of charge current leads to a counterflow of hot and cold electrons: Absence of charge current leads to a counterflow of hot and cold electrons: r B J Q ≠ 0 ; J e = 0 ; E y = 0 e - e - J Q E y r ∇ T In an ideally simple metal the Nernst effect vanishes! In an ideally simple metal, the Nernst effect vanishes! (« Sondheimer cancellation », 1948)
The Nernst coefficient is large when mobility is large and Fermi energy is small! mobility is large and Fermi energy is small! 1000 -1 ) Bi -1 T - ) ( µ V K PrFe 4 P 12 e value 10 URu 2 Si 2 absolute CeCoIn 5 CeRu 2 Si 2 ν ( a 2 2 0.1 NbSe NbSe 2 0.2 1 T(K) 10 50
Close-up on Sondheimer cancellation r r r = σ − α ∇ J e E T e r r r = α − κ ∇ J Q T E T J e =0 J e 0 Boltzmann picture: (See Oganessyan & Ussishkin, 2004) If the Hall angle Θ If the Hall angle, Θ H , does not depend on the position of the Fermi level, does not depend on the position of the Fermi level then the Nernst signal vanishes!
Roughly, the Nernst coefficient tracks ω c τ / Ε F … N ~ π 2 /3 k 2 T/e ω τ / Ε N ~ π 2 /3 k 2 B T/e ω c τ / Ε F
… and becomes large in clean semi-metals! g Bismuth URu 2 Si 2 PrFe 4 P 12 2 2 4 12 n (per f.u.) 10 -5 3 10 -2 2 10 -3
Nernst effect and superconducting fluctuations A. Pourret, H. Aubin, J. Lesueur, C. A. Marrache-Kikuchi, L. Bergé, L. Dumoulin and K. B. Nature Phys. 2 , 683 (2006) , PRB (2007)
Nernst effect in the vortex state r B E y ∇ T ∇ T • Thermal force on the vortex : Thermal force on the vortex : A superconducting vortex is: A superconducting vortex is: F=-S φ ∇ T (S φ : vortex entropy) • A quantum of magnetic flux • The vortex moves • An entropy reservoir py • The movement leads to a Th t l d t • A topological defect transverse voltage: E y =v x B z
Vortex-like excitaions in the normal state of the underdoped cuprates? underdoped cuprates? Wang, Li & Ong, ‘06 A finite Nernst signal in a wide temperature range above T c
Nernst effect due to Gaussian fluctuations of the amplitude of the superconducting order parameter amplitude of the superconducting order parameter (Usshishkin, Sondhi & Huse, PRL 2002) In 2D: In 2D: Magnetic length Magnetic length Quantum of thermo-electric conductance (21 nA/K) In two dimensions, the coherence length is the unique parameter! t ! Both the amplitude and the T-dependence of α xy is determined by ξ (T)! determined by ξ (T)!.
O Our main result: i lt 1. This theory is experimentally verified! 2. In a conventional dirty 2D superconductor, a signal due to fluctuating superconductivity can be signal due to fluctuating superconductivity can be resolved by Nernst measurements upto T~30T c .
How does it work? How does it work? • The contribution of the normal state is negligible Th t ib ti f th l t t i li ibl • Just above T c , the agreement between theory and • Just above T the agreement between theory and experimental data is better than 5 percent. • For T>>Tc [Guinzburg-Landau approximation is no more valid], the signal symmetrically depends on ξ and l B . This strongly supports a superconducting origin t l t d ti i i
Superconductivity in Nb 0.15 Si 0.85 thin films 1500 d=125 A 1200 are ( Ω ) 900 d=250 A d 250 A R squ 600 d=500 A 300 300 d=1000 A 0 0.0 0 0 0.5 0 5 1 0 1.0 1.5 1 5 2 0 2.0 2.5 2 5 3 0 3.0 3 5 3.5 4 0 4.0 T(K) The normal state is a simple dirty metal: l e ~a~ 1/k F !
A simple dirty metal subjet to weak localization l e ~ a ~k F -1 ~ 0.7 nm 1200 K F l e ~1 K F l e 1 Close to Mott-Ioffe 800 limit limit − 11 11 3 3 = ) R( Ω ) × × R R H 4 4 . 9 9 10 10 m / / C C Nb 0.15 Si 0.85 d = 12.5 nm d 5 400 400 Tc=220 mK − 11 3 = × R H 4 . 9 10 m / C ρ≅2 m Ω cm c ρ carrier density is 0 large (10 23 /cm 3 ) 0 50 100 150 200 250 300 T(K) T(K)
A Nernst signal g persists when this dirty 2D y superconductor is warmed up well p above its critical temperature ! p
Deep into the normal state!
A signal distinct from the vortex signal A signal distinct from the vortex signal
The Nernst signal of the normal electrons is negligible! Even at 6K : ν /T >> 285 ω c τ / ε F Resistivity + Hall ω c τ ∼10 −5 + Seebeck + Seebeck ε F ~10 4 K coefficients yield:
The link between ν and α xy In our case: σ xx > 10 3 σ xy σ SC < 10 -1 σ xx when T > 1.1 T c 10 σ xx when T 1.1 T c σ Therefore: α / B = ν σ = ν / R Therefore: α xy / B = ν σ xx = ν / R square
Link to the superconducting coherence length Link to the superconducting coherence length yields This should be compared to the expression for a 2D dirty superconductor: This should be compared to the expression for a 2D dirty superconductor: h v l 1 3 F F ξ ξ = = 0 0 . 36 36 d ε 2 k T Amplitude B c T d T-dependence d ε = (T-T c /T c )
The shortest link between data and v F l e F e 2 2 ⎛ ⎛ ⎞ ⎞ π κ σ k ⎜ ⎟ l B = = v 3 F ⎝ ⎝ ⎠ ⎠ γ γ γ γ T T e e e e Using specific heat and resistivity data, this yields: − − 5 2 1 v F l = × 4 . 35 10 m s
Coherence length above T c nm) 60 B ) 1/2 (n sample 2 sample 1 α xy /B 10 10 9 10 -7 = ( 5.9 2 2 ξ ξ 0.1 1 10 ε = (T-T c )/T c ε Amazing agreement for small ε!
• How about T>>T c ? Does the 6K signal How about T T c ? Does the 6K signal come from SC fluctuations?
Let us examine the field dependence! dependence!
The ghost critical field g Sample 2 Contour plot of N= -E y /(dT/dx)
A unique correlation length Contour plot of ν=Ν/Β h v l 1 3 ξ = ξ = F 0 0 . 36 36 d ε 2 k T B c
The collapse p Α unique source for the Nernst signal In the window In the window T c < T < 30T c And 0< B < 5B c2 No theory yet available!
Nernst effect and q ant m criticalit quantum criticality K. Izawa, K. B., Y. Matsuda, H. Shishido, R.Settai, Y. Onuki and J. Flouquet, Phys. Rev. Lett. 99, 147005 (2007)
The quantum critical point in CeCoIn 5 The quantum critical point in CeCoIn 5 Paglione et al. ,2003, Bianchi et al. 2003
Detected by resistivity and specific heat Paglione 2003 Bianchi 2003 Bianchi 2003
Nernst effect in the vicinity of QCP
Nernst effect in the vicinity of QCP
Nernst effect in the vicinity of QCP What is the origin of this enhancement ? A small E F ? A large Hall angle ? both?
Signatures of a small [vanishing?] E F near QCP A from Paglione et al.2003 γ from Bianchi et al.2003
No anomaly in the field-dependence of the zero -T Hall coefficient ! Singh et al. 2007
logarithmic color plot of ν /T
Energy scales near QCP Onset of T 2 Min in L/L 0 [Paglione 06] [Paglione 06] min in q=S/C
Nernst effect in bismuth Nernst effect in bismuth across the quantum limit q KB, M.-A. Méasson & Y. Kopelevich, Phys. Rev. Lett. 98, 166602 (2007) KB L Balicas & Y Kopelevich KB, L. Balicas & Y. Kopelevich, , Science 317 , 1729 (2007) Science 317 1729 (2007)
A semi-metal with a tiny Fermi surface y J.-P. Issi, Aust. J. Phys. (1979) y ( ) ε Fe = 27.6 meV Fe ε g =15.3 meV
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