Friday, March 2, 2012

Deconstructing Kondo universality

At the cake meeting this week I gave a talk on Nozieres' classic 1974 paper, A "Fermi liquid" description of the Kondo Problem at low temperatures. He gives a very elegant (but hard to follow) argument as to why the Wilson ratio should have the universal value 2, independent of the strength of the Kondo coupling J.

There is actually a clearer restatement of Nozieres' argument in a review article by Piers Coleman (see section 2.6). [I thank Ben Powell for pointing this out]. Hewson's book (Section 5.1) also has an equivalent argument but I found that even harder to follow. But, I did like the connection to Friedel's sum rule and the emphasis that the charge compressibility on the impurity site is zero.

Key assumptions (and physical insights) required in the argument seem to be:
  • A Fermi liquid fixed point (J=infinity).
  • An analytic dependence of the phase shift on energy.
  • The Kondo singlet acts as a spinless, elastic scattering centre with phase shift pi/2 at the Fermi energy.
  • The Kondo-Suhl resonance is pinned to the chemical potential.
  • For quasi-particles away from the Fermi energy only interact with quasi-particles of opposite spin.

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