1. Vortex-Nernst signal and extended phase diagram of cuprates Yayu Wang, Z. A. Xu, N.P.O (Princeton) T. Kakeshita, S. Uchida (U. Tokyo) S. Ono and Y. Ando (CRIEPI, Japan) D. A. Bonn, R. Liang, W.N. Hardy (U. Brit. Colum.) G. Gu (Brookhaven Nat. Lab.) B. Keimer (MPI, Stuttgart) Y. Onose and Y. Tokura (U. Tokyo) 1.Vortex Nernst signal above T c 2.The extended phase diagram to high fields 3.Upper critical field problem 4.Variation of H c2 vs. x LaSrCuO YBaCuO Bi 2201 Bi 2212 Bi 2223 NdCeCuO … High-fields at NHMFL, Tallahassee Supported by NSF, ONR and NEDO

2. Phase diagram of type II superconductor H T H c2 H c1 T c0 normal vortex solid liquid 0 HmHm 2H-NbSe 2 cuprates vortex solid vortex liquid ? ? HmHm 0 T T c0 H H c1 Upper critical field H c2 =  0 /2   2 H c2 coherence length  

3. Nernst experiment Vortices move in a temperature gradient Phase slip generates Josephson voltage 2eV J = 2  h n V E J = B x v

4. Nernst signal versus field at fixed T in LaSrCuO (x = 0.12) Nernst signal e y = E y / | T | Nernst coefficient v = e y / B

5. Bi 2 Sr 2-y La y Cu 2 O 6 T c = 28 K Nernst signal survives up to 80 K

6. Vortex signal above T c0 in under- and over-doped Bi 2212

7. Nernst signal extends up to T onset ~ T*/2 Vanishing of phase coherence at T c0 (RVB, Baskaran et al., ’87 Kivelson, Emery ‘95) Pseudogap state nearly degenerate with dSC Strong fluctuations between the two states T*T* 0

8. Contour plot of Nernst signal e y in T-H plane Vortex signal extends above T c0 continuously Tco Ridge field H*(T)

10. As x increases, vortex-liquid regime shrinks rapidly, H m (T) moves towards H*(T). Where is H c2 line?

11. eyey PbIn, T c = 7.2 K (Vidal, PRB ’73) Bi 2201 (T c = 28 K, H c2 ~ 48 T) T=8K H c2 T=1.5K HdHd 0.3 1.0 H/H c2 H c2 Upper critical Field H c2 given by e y 0. Hole cuprates --- Need intense fields.

12. Nernst signal in overdoped Bi 2201 in fields up to 45 Tesla

13. e y attains a T-dept. maximum, and goes to 0 at large H. By extrapolation, H c2 (0) ~ 50 Tesla. Nernst signal e y in overdoped LaSrCuO Nernst signal e y in PbIn.

14. Three field scales H m (T), H*(T), and H c2 (T). H c2 vs. T curve does not terminate at T c0 (remains large) H*H* HmHm Phase coherence lost at T c0 but  is finite T co

15. Contour plots in underdoped YBaCuO 6.50 (main panel) and optimal YBCO 6.99 (inset). T co Vortex signal extends above 70 K in underdoped YBCO, to 100 K in optimal YBCO High-temp phase merges continuously with vortex liquid state

16. Vortex-Nernst signal in Nd 2-x Ce x CuO 4 (x = 0.15) H c2 determined by e y 0 H* fixed by peak in e y e y vanishes above T c0 (unlike in hole doped)

17. Plot of H m, H*, H c2 vs. T H m and H* similar to hole-doped However, H c2 is conventional Vortex-Nernst signal vanishes just above H c2 line

18. NbSe 2 NdCeCuO Hole-doped cuprates T c0 H c2 HmHm HmHm HmHm ‘Conventional’ Amplitude transition at T c0 (BCS) Expanded vortex liquid Amplitude trans. at T c0 Vortex liquid phase is dominant. Loss of phase coherence at T c0 (zero-field melting)

19. Field scale increases as x decreases overdoped optimum underdoped

20. Vortex-Nernst signal in single-layer Bi 2201

21. Scaling of e y near T c0 Curves at T c0 obey scaling behavior e y /e y max = F(h) Allows H c2 (T c0 ) to be determined.

22. H c2 and   vs. x in Bi 2212 Coherence length vs. x Feng et al. Science, 99 Ding et al. PRL 2001 Hudson et al. PRL 2001 STM This work ARPES H c2 increases as x decreases (like ARPES gap  0 ) Compare  H (from H c2 ) with Pippard length  0 = hv F /  0 (  = 3/2) STM vortex core  STM ~ 22 A

23. Implications of H c2 vs. x Pair potential largest in underdoped (RVB theory, … Baskaran ‘87) Loss of phase coherence fixes T c0 (Emery Kivelson 1995) T c0 suppression at 0.05 not driven by competing order? ss Pair potential T c0 x ? ss Pair potential T c0 x

24. Resistivity is a bad diagnostic for field suppression of pairing amplitude Plot of  and e y versus T at fixed H (33 T). Vortex signal is large for T < 26 K, but  is close to normal value  N above 15 K.

25. Resistivity does not distinguish vortex liquid and normal state H c2

26. Summary 1. Vortex Nernst signal above T c in LaSrCuO, YBaCuO, Bi 2201, Bi 2212, Bi 2223, NdCeCuO…. 2. Contour plots of e y Smooth continuity between incoherent vortex regime and vortex liquid 3. H c2 determined in overdoped regime H c2 (0) = 50 T for x = 0.20 in LSCO H c2 vs. T does not terminate at T c0 Phase coherence lost at T c0 but H c2 and  are finite 4. H c2 vs. x determined from scaling. H c2 largest in underdoped regime

27. Appendix

28. Isolated off-diagonal Peltier current  xy versus T in LSCO Vortex signal onsets at 50 and 100 K for x = 0.05 and 0.07

29. s  =   e y /  At large H, s  goes to zero linearly. Intercept gives H c2 (T). Line entropy s  vs. H in LaSrCuO

30. Optimal, untwinned BZO-grown YBCO

31. E y = Bv x e y = Bs  /  = s    s  =   e y /  s  = “transport line-entropy” of vortex Ts  =   |M(T,H)| L D (T) near H c2 line (Caroli Maki ’68)  v H H c2 |M||M| ss 0 gradient f T = -s  T - T friction -  v -s  T

33. Nernst signal in underdoped YBaCuO (T c = 50 K) and overdoped LaSrCuO (T c = 29 K). Intrinsic field scale much higher in underdoped YBCO. Underdoped Overdoped

34. Nernst signal in overdoped LSCO and Bi 2212

37. Similar trend in Bi-2201

38. A new length scale  * Cheap, fat vortices 00 J s (r)  (r) J s (r) 00 0 0 H* = 00 2  *2 Is H* determined by close-packing of fat vortices? **

39. Temp. dependence of Nernst coef. in Bi 2201 (y = 0.60, 0.50). Onset temperatures much higher than T c0 (18 K, 26 K).

40. Charge currents in normal state (top view): J = .E and J’ = .(-  Nernst signal very small Diffusion of vortices produces Josephson E-field E = B x v

41. e y peaks within vortex state. s  linear in (H c2 - H) near H c2. Caroli-Maki Ts  =   |M(T,H)| L D (T) Ettinghausen-Nernst signal in PbIn (T c = 7.1 K)