Quantal Vortex Liquid??

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Quantal Vortex Liquid??
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Outline

• 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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Mixing TermQuasiparticle (?) phase (f)
coupling

• involves vF only (not v?)

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Mixing TermQuasiparticle (?) phase (f)
coupling

• involves vF only (not v?)
• new parameter Z quasiparticle charge

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Mixing 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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Summary 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
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StaticsIntegrate 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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Importance of ?current
Many transport phenomena (HcII(T0) boundary
of paraconductivity region of strong
superconducting fluctuations are determined by
condition When vortex cores overlap
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Importance 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??
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Importance of ?current
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H 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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Structure 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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Value 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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Dissipation
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Dissipation
Current-defined core radius
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?indep of x
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Vortex 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

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Current 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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