Friday, August 5, 2011

Deconstructing Fermi liquid scattering

What is a factor of 2 to theorists?

There is an interesting preprint The normal state of URu$_2$Si$_2$: spectroscopic evidence for an anomalous Fermi liquid by Tom Timusk and collaborators.

From a measurement of the frequency dependency of the conductivity they aim to extract the frequency and temperature dependence of the scattering rate of the Fermi liquid quasi-particles. General considerations suggest it has the form:
where omega = frequency and T=temperature. What is the value of b?
The authors find b ~ 1 but suggest that Landau would have b=4.

A few comments:

1. A fuller discussion of the theoretical literature is in a review Quantum criticality in organic conductors? Fermi liquid versus non-Fermi-liquid behaviour by Martin Dressel.
2. Hewson's book on The Kondo Problem cites work on the Anderson single impurity model which gives b=1 [see equation 5.102].

3. The Kadowaki Woods ratio [as discussed here] will be proportional to b.

4. I believe that measurements of the frequency and temperature dependence of ultrasound (zero sound) attenuation in liquid 3He are consistent with b=4.

I thank Nigel Hussey (who is currently visiting UQ) for bringing the paper to my attention.


  1. Not all experimentalists are aware of the fact that Fermi liquid theory predicts b=1 for quasiparticle scattering but b=4 for the conductivity which is a two particle process. So there is some confusion in the literature.

    My second point is that in Dressel's review several examples are given where b differs dramatically from 4. At least one of those compares the two terms, the temperature one and the frequency one, in very different energy regions. The data we quote generally makes the comparison where kT is of the order of hv. Our data meet that condition.

    My final point is that we are still looking for a system where b=4 behaviour can be observed.

    Tom Timusk

  2. Update.

    A 2013 theory paper

    shows that b=4.

    A 2014 preprint presents an analysis of optical conductivity measurements on Sr2RuO4 that are consistent with b=4