Title: Quantal Vortex Liquid??
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2Quantal Vortex Liquid??
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8Outline
- H0 Tc, ?S which states carry the current
- Vortex statics length scales
- Tc(H) and ?S(H) thermal melting of vortex
lattice and Volovik depairing - Hc(T0) quantal melting of vortex lattice
vortex viscosity and effective magnetic field - Summary and confusions.
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13Mixing TermQuasiparticle (?) phase (f)
coupling
- involves vF only (not v?)
14Mixing TermQuasiparticle (?) phase (f)
coupling
- involves vF only (not v?)
- new parameter Z quasiparticle charge
15Mixing TermQuasiparticle (?) phase (f)
coupling
- involves vF only (not v?)
- new parameter Z quasiparticle charge
Z-gt0 gtquasiparticles turn into spinons as
approach Mott phase. Small Z footprint of
spin-charge separation
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17Summary parameters
Well established values ?S0 T0
superfluid stiffness vF usual fermi
velocity roughly doping x
1.8eV-A (indep of x) Less well
established v? opening angle of gap node
??indep of x Z q.p. charge renormalization
near gap node ??indep of x
18StaticsIntegrate out fermions
Note fermions excited by T or supercurrent ? H-
field (Volovik)
T-linear penetration depth
QB1/2 so this gives Volovik effect
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43Importance of ?current
Many transport phenomena (HcII(T0) boundary
of paraconductivity region of strong
superconducting fluctuations are determined by
condition When vortex cores overlap
44Importance of ?current
Many transport phenomena (HcII(T0) boundary
of paraconductivity region of strong
superconducting fluctuations are determined by
condition When vortex cores overlap gtImportan
t question ??What do you mean by core??
45Importance of ?current
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49H in superconducting state 3 terms 1
constraint
Boson stiffness ?B(r) length scale x-1/2 size
x
Spinon stiffness ?F(r) length scale v1/? size
pFv1
Mixing term spinons feel a which couples to boson
Constraint boson, spinon currents equal, opposite
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51Structure of vortex
Short length scale boson physics solve for boson
amplitude ?(r) and gauge field a(r)
Length scale associated with current x-1/2
(see also Franz/ Tesanovic PRB63 064515 01)
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64Value of ?
- i? nc ?t? ???? acceleration of vortex
- Galilean invariance, T0accelerating vortex
drags all particles with it gtncntotal ?1 - Doped Mott insulator. T0 effective Galilean
invariance at low energy gt ncx ?1 - Conventional sc, near Tc 2 fluid ?(Tc/EF)
- RVB EF ???? J and Tc set by phase fluctgt use ?
not Tc . - D-wave nodesgtquasiparticles even at low T (high
B) suggests ???/J except perhaps as T-gt0, B-gt0
Crossover not well understood - Data (Ong) ?ltlt1 (but perhaps increasing as x-gt0)
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74Dissipation
75Dissipation
Current-defined core radius
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82?indep of x
83Vortex properties(assume 2d system for rest of
talk)
- Length scale in ?(r) must diverge as approach
Mott phase (Lee Wen PRL 78 4111 97 PRB64
224517 00) - Scale over which supercurrent can vary must
diverge as doping x-gt0 - Implication for vortex core size
84Current carried by states far from nodes?
Possible test ?S(T?)
T-dependence not useful transition is driven by
thermal phase fluctuations when ?S(Tc)2 Tc/p
(Uemura Emery/Kivelson)
KT line ?S(T)2T/p for bilayer system
But quantal flucts weaker than thermal flucts.
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