Thursday, May 19, 2011

The Hidden Fermi liquid theory

This week I have been re-reading Phil Anderson's paper,  The `strange metal' is a Fermi liquid with edge singularities. Here is a brief summary of some of the main things I gleaned from the paper. The question is:
What is the nature of the excitations (and one-electron Greens function) of the Hubbard model in the infinite-U limit and for large dopings (perhaps x greater than 0.3) above which superconductivity occurs?
Anderson claims:
  • the strong interactions lead to a significant particle-hole asymmetry [which should be visible in tunneling spectra] 
  • excitations exhibit anomalous forward scattering
  • the quasi-particle weight Z vanishes on the Fermi surface
  • there is  a formal similarity of this problem with that of Fermi-edge singularities in the X-ray spectra of metals, where the one-electron Greens function has a power law decay associated with the phase shift from an infinite potential.
  • A simple argument (exploiting the Friedel sum rule) gives the main quantitative prediction of the theory a value for the doping (x) dependence of the exponent
Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com
  • a power-law frequency dependence of the optical conductivityUnfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com
  • this theory may have some similarities to one of Norman and Chubukov.
  • Quasiparticles emerge in the superconducting and pseudogap states: "But above T* and above the gap energy the quasiparticles experience power-law decay: essentially, the line of quasiparticle poles turns into a cut in the complex  plane."

1 comment:

  1. Hi Ross,

    It's my understanding that allowing for finite mass (dispersion) of the scatterer in the X-ray edge problem cuts off the divergences giving rise to orthogonality and restores a finite residue.

    See for instance "The effect of recoil on edge singularities", P. Nozières J. Phys. I France 4 (1994) 1275-1280

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