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The NERNST EFFECT IS NOT BLACK HOLE PHYSICS

The NERNST EFFECT IS NOT BLACK HOLE PHYSICS. Wang, Li, Ong, pwa We have learned a lot about cuprates from it. OUTLINE. 1: Vortex Fluid: a distinct state of matter. defined by  s 0,  2 =0 2: Does not screen field vortices 3:Dynamics: supercurrents relax with --viscosity

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The NERNST EFFECT IS NOT BLACK HOLE PHYSICS

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  1. The NERNST EFFECT IS NOT BLACK HOLE PHYSICS Wang, Li, Ong, pwa We have learned a lot about cuprates from it

  2. OUTLINE 1: Vortex Fluid: a distinct state of matter. defined by s0, 2=0 2: Does not screen field vortices 3:Dynamics: supercurrents relax with --viscosity for vortices. 4: The Nernst Effect: e determined by viscosity, energy of vortex currents. 5: Magnitude of N E: viscosity 6: B, T dependence: d-wave gap. 7: deducing gap distribution

  3. 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 Philip Anderson: energy of int wiith field =BM/2 so M to e

  4. phase diagram

  5. Why vortex fluid in cuprates? Spin-charge locking: RVB “Gap” is electrons’ charge triad locks so that  becomes a self-energy, leaving  as a d-wave gap, which remains constant through Tc, which is a phase dis- ordering as experimentally observed. (Locking energy >>Tc) We assume a finite s and supercurrent which fluctuates in space and time, having a time correlation function We assume the pair current is conserved.

  6. theory of vortex liquid Superflows at any time described by a fluctuating tangle of vortices; with curl and div J=0, uniquely so. In the following I use the Kosterlitz-Thouless 2D model as exemplar but the key point generalizes to 3D The energy is (aside from cores) all flow energy:

  7. theory of vortex liquid cont. evaluating this using a lower cutoff a for size of vortex cores, and an upper cutoff at the sample size, gives simply This is not the expression used by K-T. They omitted the first term: assuming no net vorticity (or ignoring vortex self-energy). This one depends on sample size; or, if sample in a B-field, on R=lB, the distance between field vortices. (Feynman)

  8. Nernst magnitude calculation

  9. T=Tc e

  10. data from wang”:OD

  11. Nernst Effect Magic Formula formula for xy due to vortices note that this measures the curvature of  vs B

  12. Deducing the gap distribution The gap distibution is unknown except crudely so let’s deduce it from the magic formula instead of guessing. By calculating ey/B-dey/dB as a function of B we get a number proportional to This had better monotonically decrease with T and with B! Some “typical” data from Y Wang thesis (need low Tc to get Hc2 range, method works best for 2D underdoped)

  13. LSCO-0.07 Tc = 11K

  14. Bi2201 (La-0.7) Tc = 12K

  15. Bi2201 (La-0.2) Tc = 22K

  16. Bi2201 (La-0.4) Tc = 28K

  17. remarks and conclusion fits are very inaccurate and plagued by measurement and even systematic errors. 1: at low B and T nr Tc, crit fluctuation 2: even worse for M 3 inhomogeneity 4 but I think data support vortex fluid strongly, especially “BlnB” idea: incompressible vortex fluid 5 They also support, roughly, Fermi arc idea: the small gaps disappear first.

  18. conclusions Vortex Liquid theory gives adequate, if not precise, account of: conductivity--Timusk and Homes observations (therefore qualitative acct of Tc) Nernst Effect: magnitude and shape Questions and to be done: Is Ong-Orenstein a separate phase? I think so M(B): note nonlinearity, tracks e(B). What lies above?

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