1. 1.Introduction 2.Vortex Nernst effect 3.Enhanced Diamagnetism 4.Fragile London rigidity T>Tc 5.Low-temp. Quantum Vortex Liquid State Vorticity and the Phase Diagram of Cuprates Lu Li, J. G. Checkelsky, N.P.O. Princeton Univ. Yayu Wang, Princeton U., U.C. Berkeley M. J. Naughton, Boston College S. Ono, S. Komiya, Yoichi Ando, CRI, Elec. Power Inst., Tokyo S. Uchida, Univ. Tokyo Genda Gu, Brookhaven National Lab Hong Kong Univ, Dec. 2006

2. 1. (1975-80) Sliding charge density waves (LRA) Pinning and Depinning, FLR length 2. (1980-84) Gang of four, weak localization, Magnetoresistance, dephasing 3. (1987-2000) RVB and Gauge theories of cuprate pairing (NL, WL) 4. (1995-98) Thermal conductivity of Dirac quasiparticles Thermal Hall effect and qp-vortex scattering 5. (2000 -- ) Strong fluctuations in pseudogap state BC AD Thanks, Patrick!

3. hole s = 1/2 Phase diagram of cuprates T pseudogap 0 0.05 0.25 T*T* TcTc Mott insulator Fermi liquid doping x (fraction of sites with holes) vortex liquid dSC AF Spontaneous vorticity destroys superfluidity

4. Josephson Effect, phase-slip and Nernst signal t  VJVJ 22 Phase difference Passage of a vortex Phase diff.  jumps by 2  Integrate V J to give dc signal prop. to n v = 2  h n V Josephson Eq.

5. Nernst effect experiment Vortices move in a temperature gradient Phase slip generates Josephson voltage 2eV J = 2  h n V E J = B x v e y = E y /| T | (Nernst signal) Tc Nernst signal persists high above T c Bi 2212 (UD) Wang et al. PRB 2001

6. Giant Nernst signal in cuprates overdoped optimal underdoped Wang, Li, NPO PRB 2006 Nernst signal e N = E y /| T |

7. Vortex-Nernst signal in Bi 2201 Wang, Li, Ong PRB 2006

8. Condensate amplitude persists to T onset > T c Nernst signal confined to SC dome Vorticity defines Nernst region Nernst region

9. Kosterlitz Thouless transition in 2D superconductor Unbinding of vortex-antivortex  F = U - TS Free energy gain vortex density vortex antivortex

10. Mean-field phase diagram H 2H-NbSe 2 T H c2 H c1 T c0 normal vortex solid liquid 0 HmHm Meissner state H Cuprate phase diagram 4 T 7 K vortex solid vortex liquid H c2 TcTc 100 T 100 K HmHm Vortex unbinding in H = 0

11. 1.Vorticity persists high above T c 2.Confined to SC “dome” 3.Loss of long-range phase coherence at T c by spontaneous vortex creation (not gap closing) 4. Pseudogap intimately related to vortex liquid state Thermodynamic evidence? Implications of Giant Nernst signal

12. Supercurrents follow contours of condensate J s = -(eh/m) x |  | 2 z Diamagnetic currents in vortex liquid

13. Torque magnetometry Torque on moment:  = m × B Deflection of cantilever :  = k  crystal B m ×   Mike Naughton (Boston College)

14. Tc Underdoped Bi 2212 Wang et al. PRL 2005

15. Magnetization curves in underdoped Bi 2212 Tc Separatrix Ts Wang et al. Cond-mat/05 Wang et al. PRL 2005

16. At high T, M scales with Nernst signal e N

17. Lu Li et al., unpubl. H M M = - [H c2 – H] /  (2  2 –1) H c2 UN Bi 2212

18. “Fragile” London rigidity above Tc Above T c, M/H is singular M ~ -H 1/   is divergent) Lu Li et al. Europhys Lett 2005

19. Non-analytic magnetization above Tc M ~ H 1/  Fractional-exponent region

20. In hole-doped cuprates 1. Large region in phase diagram above Tc dome with enhanced Nernst signal 2.Associated with vortex excitations (not Gaussian) 3.Confirmed by torque magnetometry 4.Transition at T c is 3D version of KT transition (loss of phase coherence) 5. Upper critical field behavior confirms conclusion

21. Nernst region The phase diagram in x-H plane at low T H x 0 0.3 0.1 0.2 ?

22. Magnetization in lightly doped La 2-x Sr x CuO 4 Lu Li et al., unpubl. Evidence for robust diagmagnetism for x < x c

23. Lu Li et al., unpubl. Diamagnetism coexists with growing spin population Doping x

24. Lu Li et al., unpubl. Debye Waller dependence H m (T) = H 0 exp(-T/T 0 ) Vortex solid-to-liquid transition for x < x c

25. Lu Li et al., unpubl. Low temp Phase Diagram Critical Point H x 0 0.3 0.1 0.2

26. Low-temperature vortex liquid 1.Vortex solid surrounded by vortex liquid at 0.35 K 2.Sharp quantum transition at x c = 0.055. Quantum vortices destroy phase coherence 3.At 0.35 K, pair condensate survives without phase rigidity even for x = 0.03 4.Melting of vortex solid appears to be classical at 0.35 K (Debye-Waller like).

27. Summary 1.Nernst region is suffused with vorticity, enhanced diamagnetism and finite pairing amplitude 2.Extends from T c to T onset < T* 3.Nernst region dominates lower temp part of Pseudogap state 4.Depairing field H c2 and binding energy are very large Strong pairing potential but soft phase rigidity 5.Vortex-liquid state is ground state below x c Bi 2201

28. END