Nernst effect as a probe of superconducting fluctuations

Transcription

1 Nernst effect as a probe of superconducting fluctuations Kamran Behnia Ecole Supérieure de Physique et de Chimie Industrielles Paris

2 Collaborators ESPCI researchers: Alexandre Pourret, Benoît Fauqué, Aritra Banerjee, Zengwei Zhu, Huan Yang, Hervé Aubin 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)

3 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?

4 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. B hot E y J Q E x cold T S Ex xt N e y S xy E x y T [ B z E y x T ]

5 dv (nv) Set-up for monitoring thermal(k xx, k xy ), thermo-electric (S, N) and electric (s xx, s xy ) conductivity tensors Heater SC wires Thermometers T(s) DC voltages of the order of 1 nv resolved! 20 mm

6 absolute value) (V K -1 T -1 ) Nernt response of normal electrons can be very large! KB, M.A-Méasson & Y. Kopelevitch, PRL Bi PrFe 4 P URu 2 Si 2 CeCoIn CeRu 2 Si 2 NbSe T(K) 10 50

7 Semi-classical picture F H B xy e T k S T T E J T E J Q e k s 2 2 xy xx xy xx xx xy S xy s s s s If shifting the Fermi level does not change the Hall angle, then there is no Nernst signal! xy xx H s s s s 1 0 S T E J e

8 Roughly, the Nernst coefficient tracks /E F S xy B k T e H F KB, J. Phys.: Condens. Matter 21, (2009) ~ 2 /3 k B /e / E F and becomes large in clean semi-metals! Bismuth URu 2 Si 2 PrFe 4 P 12 n (per f.u.)

9 Nernst effect and superconcucting fluctuations

10 Nernst effect in the vortex state B Ey T A superconducting vortex is: A quantum of magnetic flux An entropy reservoir A topological defect Thermal force on the vortex : F=-S f T (S f : vortex entropy) The vortex moves The movement leads to a transverse voltage: E y =v x B z

11 Vortex-like excitaions in the normal state of the underdoped cuprates? Wang, Li & Ong, 06 A finite Nernst signal in a wide temperature range above T c

12 Nernst effect due to Gaussian fluctuations of the amplitude of the superconducting order parameter (Usshishkin, Sondhi & Huse, 2002) In 2D: Quantum of thermo-electric conductance (21 na/k) Magnetic length In two dimensions, the coherence length is the unique parameter! Both the amplitude and the T-dependence of xy is determined by x(t).

13 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>>T c. A. Pourret et al. Nature Phys. 2, 683 (2006); Phys. Rev. B. 76, (2007) For a review see New J. Phys., 11, (2009)

14 R square () Superconductivity in Nb 0.15 Si 0.85 thin films 1500 d=125 A d=250 A 300 d=500 A d=1000 A T(K) The normal state is a simple dirty metal: l e ~a~ 1/k F!

15 A Nernst signal persists deep into the normal state!

16 A signal distinct from the vortex signal

17 The link between and xy In our case: s xx > 10 3 s xy s SC < 10-1 s xx when T > 1.1 T c Therefore: xy / B = s xx = / R square

18 Link to the superconducting coherence length yields This should be compared to the expression for a 2D dirty superconductor: x d vf k T B c Amplitude T-dependence = (T-T c /T c )

19 The shortest link between data and v F l e s m v F e B e F e k T v s k 2 3 Using specific heat and resistivity data, this yields:

20 Coherence length above T c x= ( xy /B) 1/2 (nm) sample 2 sample = (T-T c )/T c Satisfactory agreement for small!

21 The ghost critical field Sample 2 Contour plot of N= -E y /(dt/dx)

22 A unique correlation length Contour plot of N/B x d vf k T B c

23 Why does it work so well here? The Nernst signal of the normal electrons is negligible in this dirty superconductor! In Nb 0.15 Si 0.85 mobility is small and Fermi energy is large!

24 Qunatum oscillations in Nernst response

25 Quantum oscillations of thermoelelctric coefficients in Bi KB, M.A-Méasson & Y. Kopelevitch, PRL 2007

26 S xy (mv/k) 10 1 Giant quantum oscillations K 0.46 K 0.28 K unidentified B -1 (T -1 )

27 S xy (VK -1 ) 4000 Quantum oscillations in graphite Zhu et al., Nature Physics, Nov K 1000 HOPG sample 1 8 K 4.2 K HOPG sample K 1.6 K 1.65 K 0.98K 0.77 K B(T) 0.55 K 0.34 K 0.29 K

28 Quantum oscillations in Graphene Zuev, Chang & Kim, PRL 09 When a Landau level meets the Fermi level, S xy vanishes! See also: Wei et al., PRL 09 Checkelsky and Ong, arxiv:

29 Theory for 2DEG Oji, J. Phys. C 84 Jonson & Girvin, PRB 84

30 S xy (V/K) Nernst Signal V y (nv) bismuth 1000 Empirical correlation between the Nernst profile and dimensionality! nv, 312mK nv, 475mk nv, 760mK nv, 910mK GaAs 3D 2D 100 graphite B -1 (T -1 ) 0.343K 0.549K 0.678K 0.771K 0.805K 0.853K 0.976K 1.651K graphene B -1 (T -1 )

31 A topological phase transition in 3D Zhu et al., Nature Physics 09 For a review paper on topological phase transitions, see: Blanter, Kaganov, Pantsulaya and Varlamov Phys. Rep. 245, 159 (1994).

32 What happens beyond the quantum limit? The quantum limit (9T)

33 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

34 Bismuth T=1.5 K Length scales and Nernst coefficient in Bi

35 A surprise at still higher fields! Fauqué et al. New J. Phys (2009) No more Landau level crossing is expected!

36 All these states are expected to deteriorate metallicity!

37 The hig-field anomaly looks like a LL crossing! The T-dependence confirms a hole-ellipsoid origin! No critical temperature!

38 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 Examples: SC, DW, The ground state is a quantum liquid No order parameter No critical temperature Examples: QHE (Integer and fractional)

39 Summary Nernst effect is a sensitve probe of : superconducting fluctuations quantum oscillations 3D metal beyond the quantum limit

40 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?

41 Electron spectrum in bismuth at high field The magnetic field displaces the Fermi Energy, in order to preserve charge neutrality: n h =n e1 +n e2 +n e3 Sharlai & Mikitik PRB 2009

42 A very anisotropic field scale associated with electron pockets Experiment Sharalai & Mikitik, PRB 09 Alicea & Balents PRB 09 Lu Li et al., Science 08

43 Are the high-field Nernst peaks a result of small misalignment? Sharalai & Mikitik, PRB 09 In case of perfect alignment, no anomaly beyond 10T is expected!

44 Are the high-field Nernst peaks a result of small misalignment? Sharalai & Mikitik, PRB 09 But there is an arbitrary angle for which three high-field e - anomalies are expected!

45 Angular dependent Nernst effect H. Yang et al., unpublished

46 Field (Teslas) Angular dependent Nernst effect B. Fauqué, LNCMI-Grenoble 3 AM 10 /09/09 ANGLE (DEGREES)

47 Angular dependent Nernst effect?? 0 + e 1 - e Quasi- horizontal lines and quasi-vertical lines

48 When the field is aligned along trigonal The temperature dependence confirms an e - ellipsoid origin!

49 HOPG and natural graphite

50 Thermopower and Nernst effect in graphite

51 Non-trivial Berry phase in graphite