Inhomogeneity and phase

Transcript

1 Inhomogeneity and phase fluctuations in lowdimensional superconductors Lara Benfatto* Centro Fermi and Universiy of Rome La Sapienza * www:

2 Claudio Castellani University of Rome La Sapienza Thierry Giamarchi University of Geneva L.Benfatto, C. Castellani and T. Giamarchi, PRL 98, (07) L.Benfatto, C. Castellani and T. Giamarchi, PRL 99, (07) L.Benfatto, C. Castellani and T. Giamarchi, PRB 77, (R) (08) L.Benfatto, C. Castellani and T. Giamarchi, in preparation

3 FAQ about inhomogeneity & superconductivity What is inhomogeneous??? When is it more relevant? Is it a common characteristic of different systems? The case of quasi-2d superconductors A not universal Kosterlitz Thouless physics Role of inhomogeneity

4 Kosterlitz-Thouless physics in 2D SC J.M.Kosterlitz and D.J.Thouless, J. Phys. C (1973, 1974) Crucial role of phase fluctuations in 2D Two regimes: 1. Low T: superfluidity ψ ( r ) = e iθ 2. High-T: vortices proliferate and destroy superfluid stiffness Usual approach: XY model vortex-core energy µ

5 Signatures of Kosterlitz-Thouless transition In the superconducting state Universal jump of the superfluid density at T KT π 2T He4 films McQueeney et al. PRL 52, 1325 (84)

6 Signatures of Kosterlitz-Thouless transition In the superconducting state Universal jump of the superfluid density at T KT π 2T The universality is NOT affected by the precise value of the vortex-core energy µ

7 Signatures of Kosterlitz-Thouless transition In the superconducting state Universal jump of the superfluid density at T KT Above the superconducting state Effect of the superconducting fluctuations on the physical quantities, like Resistivity Magnetization Nerst effect

8 Do we have any chance to really see KT physics? Let s look from above Superconducting fluctuations are described in terms of the correlation length ξ Amplitude fluctuations (Ginzburg-Landau theory) T KT T c0 T KT phase fluctuations as due to vortices Very difficult to see KT fluctuations if this interval is very small!!

9 KT physics in 3D HTSC? Layered anisotropic systems J c Large anisotropy: J c each plane is an independent 2D unit Low superfluid density: c J ab J << ab T c J J ab KT regime is more easily accessible KT physics in bulk systems

10 Do we have any chance to really see KT physics?? Let s look from below.. Decreasing doping J s (0) ~ T c In principle, HTSC are the best candidate to see KT physics (if any) T Glassy09 c0 -T KT large Lara Benfatto

11 Experiments in High-Tc superconductors

12 Nerst effect: vortex fluctuations Large Nerst signal above T c attributed to thermally diffusing vortices Y. Wang, L. Li and N. P. Ong, PRB 73, (2006);

13 Correlation length Correlation length is of KT type! UD Bi2212 But no signature AT ALL of KT physics in the resistivity measurements S.Caprara et al. PRB 72, (05) B. Leridon et al, PRB 76, (06) T KT T c L. Li et al, EPL 72, 451 (2005)

14 ..what about the superfluid density? Possible signature of the jump in strongly anisotropic compounds: Hg-1223 C. Panagopoulos et al. PRB 53, 2999(R) (96); PRL 79, ) π 2T

15 ..what about the superfluid density? No signature at all at the supposed to be T KT in strongly underdoped YBCO samples with LARGE anisotropy (J c /J ab ~10-4 ) YBCO D.Broun et al, PRL 99, (07) π 2T

16 ..what about the superfluid density? No sharp signature of the universal jump even in ultrathin films of strongly underdoped YBCO I.Hetel, T.R.Lemberger and M.Randeria, Nat. Phys. 3, 700 (2007) π 2T

17 Is there really a problem? From above T c : vortex fluctuations, with KT character From above T c :no downturn of the superfluid density at the T KT estimated from the UNIVERSAL 2D jump No sharp transition even in truly 2D case No KT physics but only Standard Cooper pairs GL fluctuations

18 Is there really a problem? From above T c : vortex fluctuations, with KT character From above T c :no downturn of the superfluid density at the T KT estimated from the UNIVERSAL 2D jump No sharp transition even in truly 2D case Experiments Theory Lack of a general knowledge of KT physics in the presence of J c, B and inhomogeneity

19 why do we expect to see some signature in the superfluid density at the same universal value of the 2D system also in the layered anisotropic case?

20 because XY model is our paradigm! A single energy scale J exists µ= vortex-core energy µ ~ J, T KT ~ J T V ~ T KT

21 because XY model is our paradigm! A single energy scale J exists + J c µ= vortex-core energy µ ~ J, T KT ~ J T C ~ T KT Cataudella, Minnaghen, Physica C (90); M. Friesen PRB (1995); S.W.Pierson PRB (1995); P.Minnaghen & Olsson PRB (91) B.Chattopadhyay & S.R.Shenoy PRL (94)

22 because XY model is our paradigm! A single energy scale J exists + J c µ= vortex-core energy µ ~ J, T KT ~ J What happens is µ is an independent energy scale? Competing state in the vortex core? We need to go beyond the pure XY model Same problem for QUANTUM effects: L.B., A.Toschi, S.Caprara and C.Castellani, PRB 64, (01); PRB 66, (02); PRB 69, (04)

23 A general methodology issue We want to study the Kosterlitz-Thouless physics in the presence of a relevant perturbation (interlayer coupling) by allowing for vortex-core energy µ independent of J + J c Mapping to the sine-gordon model Renormalization Group approach

24 The superfluid density: no universal behavior! 2D: one relevant perturbation (in RG sense): Vortex unbinding tends to kill superfluidity at T=T KT

25 The superfluid density: no universal behavior! + J c Layered: two relevant perturbations (in RG sense): Vortex unbinding tends to kill superfluidity at T=T KT Josephson coupling tends to keep the system superfluid The transition occurs when vortex unbinding predominates over the interlayer-coupling: the scale is NOT UNIVERSAL J c

26 The superfluid density: no universal behavior! L.Benfatto, C. Castellani and T. Giamarchi, PRL 98, (07)

27 Estimate of the vortex-core energy Two-unit-cells thick underdoped YBCO films: the transition IS of KT type! I.Hetel, T.R.Lemberger and M.Randeria, Nat. Phys. 3, 700 (2007) n=1 n=2 The crossover from T KT n=1 to T KT n=2 is induced by an increase of µ

28 Doping dependence of the vortex-core energy We reproduce the data using J fixed and µ as the only fitting parameter (+ Tc inhomogeneity) with underdoping µ increases with respect to the single-layer stiffness T c moves away from the T KT of the single layer L.Benfatto, C.Castellani and T.Giamarchi, PRB 77, (R) (2008)

29 Role of the inhomogeneity Large dissipative peak and long tail: cannot be explained as a finite-frequency (50 Khz) effect

30 Role of the inhomogeneity Large dissipative peak and long tail: cannot be explained as a finite-frequency effect

31 Role of the inhomogeneity Large dissipative peak and long tail: cannot be explained as a finite-frequency effect K.K.Gomes, et al. Nature 447, 569 (2007)

32 Role of the inhomogeneity Large dissipative peak and long tail: cannot be explained as a finite-frequency effect The same effect has been seen in strongly underdoped YBCO Inhomogeneity increases with decreasing the superfluid-density How general is this effect??? D.Broun et al. PRL 99, (2007)

33 Superconductivity in Heterostructures A.Caviglia et al. Nature 456, 624 (08) change of doping by field effect N. Reyren et al, Science 317, 1196 (2007) REAL 2D system: 15 nm thick SC layer of doped SrTiO 3 Need to account for finite-size effects + inhomogeneity

34 Analysis of resistivity Superconducting fluctuations RG study of the correlation length: the approximate form T KT T c0 T is valid ONLY when Finite size effects + inhomogeneity

35 Inhomogeneity in SC heterostructures A GL+KT fit shows that T KT ~ T c0 Tails in the resistivity arise from inhomogeneity T KT T c0 T KT T c0

36 Inhomogeneity in SC heterostructures A GL+KT fit shows that T KT ~ T c0 Tails in the resistivity arise from inhomogeneity

37 Inhomogeneity in SC heterostructures A GL+KT fit shows that T KT ~ T c0 Tails in the resistivity arise from inhomogeneity Inhomogeneity is more relevant when disorder increases and low-t superfluid density decreases

38 Inhomogeneity in SC heterostructures A GL+KT fit shows that T KT ~ T c0 Tails in the resistivity arise from inhomogeneity Inhomogeneity is more relevant when disorder increases and low-t superfluid density decreases

39 Summary about the mistery of KT physics KT physics in layered superconductors: if it is at play, one has to take into account that it can have a NOT UNIVERSAL character (it is also true on the case of magnetic field: see L.B. et al. PRL 99, (07)

40 FAQ about inhomogeneity & superconductivity What is inhomogeneous??? (superfluid) density When is it more relevant? When average superfluid density gets very small Is it a common characteristic of different systems? Yes: so we may have a chance to understand its origin in those cases where we do not have competing phases