What lies above : the vortex liquid above T c in cuprate - PowerPoint PPT Presentation

What lies above : the vortex liquid above T c in cuprate superconductors. Yayu Wang, LuLi, J. Checkelsky, N.P.O. Princeton Univ. M. J. Naughton, Boston College 1. Vortex Nernst effect 2. Loss of long-range phase coherence 3. The Upper Critical Field 4. High-temperature Diamagnetism 5. KT vs 3DXY: phase-correlation length S. Uchida, Univ. Tokyo Yoichi Ando, Elec. Power U., Tokyo Genda Gu, Brookhaven S. Onose, Y. Tokura, U. Tokyo B. Keimer, MPI Stuttgart Les Diablerets Sep 2005

Phase diagram of Cuprates Mott insulator s = 1/2 hole T * T pseudogap T c Fermi liquid AF dSC 0 0.25 0.05 doping x

� Nernst experiment e y H m H Nernst signal Vortices move in a temperature gradient Phase slip generates Josephson voltage e y = E y /| T | 2 eV J = 2 π h n V E J = B x v

Nernst effect in underdoped Bi-2212 (T c = 50 K) Vortex signal persists to 70 K above T c !

Nernst curves in over, optimal and underdoped Bi 2201 underdoped overdoped optima l

Phase rigidity | Ψ | e i θ ( r ) Long-range phase coherence requires uniform θ “kilometer of dirty lead wire” θ θ θ θ phase rigidity measured by ρ s Phase coherence destroyed by vortex motion θ θ Emery, Kivelson, (1995): Spontaneous vortex creation at Tc in cuprates

Overall scale of Nernst signal amplitude

•Loss of phase coherence determines Tc •Condensate amplitude persists T>Tc

Hole-doped cuprates NbSe 2 NdCeCuO H c2 H c2 H c2 vortex vortex liquid liquid H m H m H m T c0 T c0 T c0 Vortex liquid dominant. Expanded vortex liquid Conventional SC Loss of phase coherence Amplitude vanishes at Amplitude vanishes at T c0 (zero-field melting) T c0 at T c0 (BCS)

Hole-doped optimal Electron-doped optimal

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

Vortex-Nernst signal in Bi 2201

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

Cantilever torque magnetometry Torque on magnetic moment: τ = m × B crysta l B τ × φ m Deflection of cantilever : τ = k φ

Tc

T c 110K • In underdoped Bi-2212, onset of diamagnetic fluctuations at 110 K • diamagnetic signal closely tracks the Nernst effect

Magnetization curves in underdoped Bi 2212 Tc Separatrix Ts

At high T, M scales with Nernst signal e N

Magnetization in Abrikosov state M H H c1 H c2 M = - [H c2 – H] / β (2 κ 2 –1) M~ -lnH In cuprates, κ = 100-150, H c2 ~ 50-150 T M < 1000 A/m (10 G) Area = Condensation energy U

H c2 H c2 M T T c - T c In conventional type II supercond., H c2 0 H c2 H c2 M T c In cuprates, H c2 is unchanged as T T c

Resistivity Folly Bardeen Stephen law (not seen) H c2 H c2 Resistivity does not distinguish vortex liquid and normal state

Phase fluctuation in cuprate phase diagram spin pairing (NMR relaxation, T* Bulk suscept.) pseudogap Temperature T T onset Onset of charge pairing Vortex-Nernst signal Enhanced diamagnetism Kinetic inductance vortex liquid T c superfluidity long-range phase coherence Meissner eff. 0 x (holes)

Relevant Theories Baskaran et al. (Sol. St. Comm. ‘87); Kotliar and Liu (Phys. Rev. B ‘88) Phase diagram, Tc vs x, and Mott limit Emery Kivelson (Nature 95) Loss of coherence at Tc in low (superfluid) density SC’s M. Renderia et al. (Phys. Rev. Lett. ’02) Cuprates in strong-coupling limit, distinct from BCS limit. Tesanovic and Franz (Phys. Rev. B ’99, ‘03) Strong phase fluctuations in d-wave superconductor treated by dual mapping to Bosons in Hofstadter lattice --- vorticity and checkerboard pattern Balents, Sachdev, Fisher et al. (2004) Vorticity and checkerboard in underdoped regime P. A. Lee, X. G. Wen. (PRL, ’03, PRB ’04) Loss of phase coherence in tJ model, nature of vortex core P. W. Anderson (cond-mat ‘05) Spin-charge locking occurs at T onset > T c

M vs H below Tc Full Flux Exclusion Strong Curvature! Hc 1 -M H

Strong curvature persists above Tc

M non-analytic in weak field M ~ H 1/ δ

Susceptibility and Correlation Length Strongly H-dependent Susceptibility χ = M/H Fit to Kosterlitz Thouless theory χ = -(k B T/2d φ 0 2 ) ξ ΚΤ 2 ξ ΚΤ = a exp(b/t 1/2 )

Non-analytic magnetization above Tc M ~ H 1/ δ Fractional-exponent region

Anomalous high-temp. diamagnetic state 1. Vortex-liquid state defined by large Nernst signal and diamagnetism 2. � M ( T,H ) closely matched to e N ( T,H ) at high T ( β is 10 3 - 10 4 times larger than in ferromagnets). 3. � M vs. H curves show H c2 stays v. large as T à T c . 4. Magnetization evidence that transition is by loss of phase coherence instead of vanishing of gap 5. Nonlinear weak-field diamagnetism above T c to T onset . 6. NOT seen in electron doped NdCeCuO (tied to pseudogap physics)

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