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Introduction Vortex Nernst effect Enhanced Diamagnetism Fragile London rigidity T>Tc

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.

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Introduction Vortex Nernst effect Enhanced Diamagnetism Fragile London rigidity T>Tc

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  1. Vorticity and the Phase Diagram of Cuprates Lu Li,J. G. Checkelsky, N.P.O. Princeton Univ. Yayu Wang, PrincetonU.,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 • Introduction • Vortex Nernst effect • Enhanced Diamagnetism • Fragile London rigidity T>Tc • Low-temp. Quantum Vortex Liquid State Hong Kong Univ, Dec. 2006

  2. BC AD Thanks, Patrick! • 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

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

  4. = 2ph nV 2p f Integrate VJ to give dc signal prop. to nv VJ t Josephson Effect, phase-slip and Nernst signal Passage of a vortex Phase diff. f jumps by 2p Josephson Eq. Phase difference

  5. Vortices move in a temperature gradient Phase slip generates Josephson voltage 2eVJ = 2ph nV EJ = B x v ey = Ey /| T | Wang et al. PRB 2001 Nernst effect experiment Bi 2212 (UD) Tc Nernst signal persists high above Tc (Nernst signal)

  6. Giant Nernst signal in cuprates Wang, Li, NPO PRB 2006 Nernst signal eN = Ey /| T | underdoped optimal overdoped

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

  8. Nernst region • Condensate amplitude persists to Tonset > Tc • Nernst signal confined to SC dome • Vorticity defines Nernst region

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

  10. normal liquid Hm Hc2 vortex solid Hc1 0 Tc0 T Mean-field phase diagram Cuprate phase diagram 2H-NbSe2 4 T 100 T Hc2 H H vortex liquid Hm Tc vortex solid Vortex unbinding in H = 0 100 K 7 K Meissner state

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

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

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

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

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

  16. At high T, M scales with Nernst signal eN

  17. Hc2 M H M = - [Hc2 – H] / b(2k2 –1) Lu Li et al., unpubl. UN Bi 2212

  18. “Fragile” London rigidity above Tc Lu Li et al. Europhys Lett 2005 Above Tc, M/H is singular M ~ -H1/d (c is divergent)

  19. Non-analytic magnetization above Tc M ~ H1/d Fractional-exponent region

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

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

  22. Magnetization in lightly doped La2-xSrxCuO4 Lu Li et al., unpubl. Evidence for robust diagmagnetism for x < xc

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

  24. Vortex solid-to-liquid transition for x < xc Lu Li et al., unpubl. Debye Waller dependence Hm(T) = H0 exp(-T/T0)

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

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

  27. Summary • Nernst region is suffused with vorticity, • enhanced diamagnetism and • finite pairing amplitude • Extends from Tc to Tonset < T* • Nernst region dominates lower temp part of • Pseudogap state • 4. Depairing field Hc2 and binding energy are • very large • Strong pairing potential but soft phase rigidity • 5. Vortex-liquid state is ground state below xc Bi 2201

  28. END

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