The case against inhomogeneous superconductivity (granular Al) Vortex-liquid boundary linear in x as x 0? dissipative, vortices mobile Long-range phase coherence Sharp transition in Tc vs x (QCT?) Magnetization in lightly doped La2-xSrxCuO4 Lu Li et al., unpubl. Two distinct field scales In ground state, have 2 field scales 1) Hm(0) ~ 6 T Dictates phase coherence, flux expulsion 2) Hc2(0) ~ 50 T Depairing field. Pinning current reduced by a factor of ~100 in ground state Loss of phase coherence at TcĬomparison between x = 0.055 and 0.060 Sharp change in ground state Lu Li et al., unpubl. + - + Hc2 vortex liquid Hm Tc Signature features of cuprate superconductivity 1. Upper critical field Behavior of Hc2(T) not mean-field. 2.Scaling with Nernst Above Tc, magnetization M scales as eN vs. Magnetization in Abrikosov state M H Hc1 Hc2 M = - / b(2k2 –1) M~ -lnH In cuprates, k = 100-150, Hc2 ~ 50-150 T M 45 T. M(T,H) matches eN in both H and T above Tc (excitation of vortices)Īt high T, M scales with Nernst signal eN Y2 y1 y2 y1 Anderson-Higgs mechanism: Phase stiffness singular phase fluc. Magnetization curves in underdoped Bi 2212 Wang et al. Paramagnetic background in Bi 2212 and LSCO ~100 times more sensitive than commercial SQUID.Sensitivity: ~ 5 × 10-9 emu at 10 tesla.Si single-crystal cantilever Micro-fabricated single crystal silicon cantilever magnetometer H × B m Cantilever torque magnetometry Torque on magnetic moment: = m × B crystal Deflection of cantilever: = k Js = -(eh/m) x |Y|2 z Diamagnetic currents in vortex liquid Supercurrents follow contours of condensate Pseudogap intimately related to vortex liquid state More direct (thermodynamic) evidence? by spontaneous vortex creation (not gap closing).Loss of long-range phase coherence at Tc.Upper critical field Hc2 versus T is anomalous.Existence of vortex Nernst signal above Tc.Vorticity and diamagnetism in Nernst region.Rs D 0 TKT TcMF Kosterlitz-Thouless transition Spontaneous vortices destroy superfluidity in 2D films Change in free energy DF to create a vortex DF = DU– TDS = (ec – kBT) log (R/a)2 DF TKT = ec/kB vortices appear spontaneously 3D version of KT transition in cuprates? Nernst signal eN = Ey /| T | Nernst curves in Bi 2201 Yayu Wang,Lu Li,NPO PRB 2006 underdoped optimal overdoped Wang, Li, Ong PRB 2006 Vortex-Nernst signal in Bi 2201 Nernst effect in underdoped Bi-2212 (Tc = 50 K) Nernst signal ey = Ey /| T | Vortices move in a temperature gradient Phase slip generates Josephson voltage 2eVJ = 2ph nV EJ = B x v Nernst experiment ey Hm H to nv VJ t The Josephson Effect, phase-slippage and Nernst signal Passage of a vortex Phase diff. Phase difference vortex 2p f Integrate VJ to give dc signal prop. 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 100 K 7 K Meissner state Q q q q q q Phase rigidity ruined by mobile defects Long-range phase coherence requires uniform q “kilometer of dirty lead wire” phase rigidity measured by rs Phase coherence destroyed by vortex motion Kosterlitz Thouless transition in 2D films (1982)ī(r) Normal core Js x x b(r) |Y| = D London length l Vortices, fundamental excitation of type-II SC Vortex in cuprates Vortex in Niobium CuO2 layers superfluid electrons Js 2D vortex pancake H coherence length x Mott insulator T* T pseudogap Tc Fermi liquid AF dSC 0 0.25 0.05 doping x Phase diagram of Cuprates s = 1/2 hole LSCO = La2-xSrxCuO4 Bi 2212 = Bi2Sr2CaCu2O8 Bi 2201 = Bi2-yLaySr2CuO6Ĭondensate described by a complex macroscopic wave function Y(r) = Y1 + iY2 = |Y(r)| exp y2 y1 y2 y1 Anderson-Higgs mechanism: Phase stiffness singular phase fluc.
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