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

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

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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

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SLIDE 1
  • 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

What lies above: the vortex liquid above Tc in cuprate superconductors.

Yayu Wang, LuLi, J. Checkelsky, N.P.O. Princeton Univ.

  • M. J. Naughton, Boston College

Les Diablerets Sep 2005

  • S. Uchida, Univ. Tokyo

Yoichi Ando, Elec. Power U., Tokyo Genda Gu, Brookhaven

  • S. Onose, Y. Tokura, U. Tokyo
  • B. Keimer, MPI Stuttgart
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SLIDE 2

hole s = 1/2

Phase diagram of Cuprates

T pseudogap

0.05 0.25 AF

dSC T* Tc Mott insulator Fermi liquid doping x

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SLIDE 3

Nernst experiment

Vortices move in a temperature gradient Phase slip generates Josephson voltage

  • 2eVJ = 2πh nV

EJ = B x v

H ey Hm

Nernst signal

ey = Ey /| T |

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SLIDE 4

Nernst effect in underdoped Bi-2212 (Tc = 50 K)

Vortex signal persists to 70 K above Tc !

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SLIDE 5

Nernst curves in over, optimal and underdoped Bi 2201

  • verdoped
  • ptima

l underdoped

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SLIDE 6

Phase rigidity

Long-range phase coherence requires uniform θ

|Ψ| eiθ(r)

Phase coherence destroyed by vortex motion

θ θ θ θ

“kilometer of dirty lead wire”

phase rigidity measured by ρs

θ θ

Emery, Kivelson, (1995): Spontaneous vortex creation at Tc in cuprates

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SLIDE 7

Overall scale of Nernst signal amplitude

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SLIDE 8
  • Loss of phase coherence determines Tc
  • Condensate amplitude persists T>Tc
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SLIDE 9

NbSe2 NdCeCuO Hole-doped cuprates Tc0 Tc0 Tc0 Hc2 Hc2 Hc2 Hm Hm Hm

Expanded vortex liquid Amplitude vanishes at Tc0 Vortex liquid dominant. Loss of phase coherence at Tc0 (zero-field melting) Conventional SC Amplitude vanishes at Tc0 (BCS)

vortex liquid vortex liquid

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SLIDE 10
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SLIDE 11

Hole-doped optimal Electron-doped optimal

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SLIDE 12

ey

PbIn, Tc = 7.2 K (Vidal, PRB ’73) Bi 2201 (Tc = 28 K, Hc2 ~ 48 T)

T=8 K Hc2 T=1.5K Hd

0.3 1.0 H/Hc2 Hc2

  • Upper critical Field Hc2 given by ey 0.
  • Hole cuprates --- Need intense fields.
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SLIDE 13

Vortex-Nernst signal in Bi 2201

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SLIDE 14
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SLIDE 15

Supercurrents follow contours of condensate H Js = -(eh/m) x |Ψ|2 z

Diamagnetic currents in vortex liquid

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SLIDE 16

Cantilever torque magnetometry

Torque on magnetic moment: τ = m × B

Deflection of cantilever: τ = k φ

crysta l B

m

× τ

φ

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SLIDE 17

Tc

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SLIDE 18
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SLIDE 19
  • In underdoped Bi-2212, onset of diamagnetic fluctuations at 110 K
  • diamagnetic signal closely tracks the Nernst effect

110K Tc

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SLIDE 20

Magnetization curves in underdoped Bi 2212 Tc Separatrix Ts

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SLIDE 21
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SLIDE 22

At high T, M scales with Nernst signal eN

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SLIDE 23

Magnetization in Abrikosov state H M

M~ -lnH

M = - [Hc2 – H] / β(2κ2 –1) Hc2 Hc1 In cuprates, κ = 100-150, Hc2 ~ 50-150 T M < 1000 A/m (10 G) Area = Condensation energy U

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SLIDE 24
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SLIDE 25
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SLIDE 26

Hc2 Tc In conventional type II supercond., Hc2 0 T Tc- Hc2 M Hc2 M In cuprates, Hc2 is unchanged as T Tc Hc2 Tc

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SLIDE 27
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SLIDE 28

Resistivity does not distinguish vortex liquid and normal state Hc2 Hc2

Bardeen Stephen law (not seen)

Resistivity Folly

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SLIDE 29

T* Tonset Tc

spin pairing (NMR relaxation, Bulk suscept.) vortex liquid Onset of charge pairing Vortex-Nernst signal Enhanced diamagnetism Kinetic inductance superfluidity long-range phase coherence Meissner eff.

x (holes) Temperature T Phase fluctuation in cuprate phase diagram pseudogap

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SLIDE 30

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 Tonset > Tc

Relevant Theories

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SLIDE 31

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

  • M

H

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SLIDE 32

Strong curvature persists above Tc

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SLIDE 33

M ~ H1/δ M non-analytic in weak field

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SLIDE 34

Fit to Kosterlitz Thouless theory χ = -(kBT/2dφ0

2) ξΚΤ 2

ξΚΤ = a exp(b/t1/2) Strongly H-dependent Susceptibility χ = M/H Susceptibility and Correlation Length

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SLIDE 35

Non-analytic magnetization above Tc M ~ H1/δ Fractional-exponent region

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SLIDE 36

Anomalous high-temp. diamagnetic state

  • 1. Vortex-liquid state defined by large Nernst signal and

diamagnetism 2. M(T,H) closely matched to eN(T,H) at high T (β is 103 - 104 times larger than in ferromagnets). 3. M vs. H curves show Hc2 stays v. large as Tà Tc. 4. Magnetization evidence that transition is by loss of phase coherence instead of vanishing of gap 5. Nonlinear weak-field diamagnetism above Tc to Tonset. 6. NOT seen in electron doped NdCeCuO (tied to pseudogap physics)

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SLIDE 37

End