Nernst signal in low-Tc disordered superconductors Alexandre Pourret

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 Nbx. Si 1 -x Observation of a non-zero Nernst signal above. Tc Origin of the Nernst signal above Tc Comparison with theoritical prediction III. The In. Ox case Comparison with Nbx. Si 1 -x

Thermoelectric coefficients Thermoelectric power JQ Nernst signal Nernst coefficient

Sondheimer cancellation (1948) Counterflow of hot and cold electrons e- e. B e- e- e- e. JQ≠ 0; Je=0; Ey=0 e- e. Hot side Cold side T In an ideally simple metal, the Nernst effect vanishes!

Roughly, the Nernst coefficient tracks m/ e. F… Boltzmann equation mobility Low Fermi Energy = high Nernst signal!

Recipe for a large diffusive Nernst response: • High mobility • Small Fermi energy • Ambipolarity

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 q q 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 k and electrical conductivity s. 4 mm Heater Thermometers Sample Silver/Gold wire Cooper block Ø 1. 5 cm

Nbx. Si 1 -x : an homogenous amorphous superconductor Co-evaporation of Nb and Si. No granularity observed by AFM r=2 m. Wcm Two samples 12. 5 nm and 35 nm sample Quartz Nb Quartz Si Ecran Si Nb le~ a ~k. F-1~ 0. 7 nm k. F le ~1 Close to Mott-Ioffe limit carrier density is large (1023 /cm 3)

Superconductivity in Nb 0. 15 Si T(K) 0. 85 thin films

Above Tc, Cooper pairs fluctuations Paraconductivity Nernst effect can detect Cooper pairs fluctuations up to 30 * Tc. Theory : Fluctuations described in Gaussian approximation -Aslamazov – Larkin; Physics Letters, 26 A, 238 (1968) -Maki-Thomson -Density of States

Magnetic field induced Quantum Superconductor. Insulator transition (Field perpendicular to sample plane) nz~0. 7 Finite size scaling Paraconductivity T c H. Aubin et al. PRB 73, 094521 (2006)

Nernst signal above Tc (d=12. 5 nm , Tc=165 m. K) in sample 1 A. Pourret et al. Nature Physics 2, 683 (2006) Finite Nernst signal up to T=30*Tc and B>Bc 2 (0. 85 T)

Nernst coefficient in sample 1 (Tc =165 m. K) n is independent of magnetic field at low magnetic field

Nernst signal below and above Tc (Sample 2, TC =380 m. K) A signal distinct from the vortex signal TTc

Two characteristic fields that evolve symmetrically with respect to critical temperature m. V/K Landau quantization of the fluctuating Cooper pair motion Below Tc : Bc 2 Above Tc : B*

Normal state Nernst signal is very weak nn < S tan. Q, Q Hall angle The Cooper pairs life time is larger than the quasi particles life time : t. GL= tqp ( x/le) 2

Why a dirty superconductor? Compare the Ginzburg-Landau time scale and the quasi-particle lifetime: t. GL= tqp ( x/le) 2 t dirty t. GL> tqp t dirtier 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 2 D At low magnetic field Close to Tc Quantum of thermoelectric conductivity (21 n. A/K) sxx > 103 sxy et s. SC < 10 -1 sxx BCS correlation length : With Marnieros (2000) Precise prediction Reduced temperature:

Comparaison with theoretical prediction is independent of the magnetic field at low field. The amplitude of signal is consistent with theory , close to Tc (B->0), with no adjustable parameters. Sample 2 Tc=380 m. K

The Nernst signal is determined only by the size of superconducting fluctuations m. V/KT A. Pourret et al. PRB 76, 214504 (2007). d(nm) Pour B>B*, the caracteristic length is l. B Pour B

Nernst signal is sensible to x x= l. B x d= l B x= xd x generalized correlation length

The magnitude of the Nernst coefficient at high magnetic field can be predicted The same function F(x) determine axy/B: With x= xd for B < And B* x= l. B for B > B* Landau quantization of the fluctuating Cooper pair motion µ xd 2 B=0 µ xd 4

At Tc, Nernst coefficient is determined by l. B on the whole magnetic field range, because xd diverge F (l. B) corresponds to

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 In. Ox M. A. Paalanen et al. Phys. Rev. Lett. 69, 1604 (1992). V. F. Gantmakher et al. JETP Lett. 61, 606 (1995). G. Sambandamurthy et al. Phys. Rev. Lett. 92, 107005 (2004). V. F. Gantmakher, et al. JETP Lett. 71, 160 (2000). SIT n Low carrier density: n=1021 cm-3 Weak phase stiffness (Emery and Kivelson) Ovadyahu Z. Superconductor Bose Insulator Metal

Nb 0. 15 Si 0. 85 In. Ox

The coherence length doesn’t diverge

The case of In. Ox Carrier density is 80 times lower than Nb 0. 15 Si 0. 85 Strong phase fluctuations • No visible anomaly in axy(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~30 Tc in a dirty superconducting film! The magnitude of the signal is in very good agreement with theory. The field dependence of this signal detects the “ghost critical field”, confirming a superconducting origin.