Friday, August 19, 2011

Signatures of a non-Fermi liquid

Two signatures of a Fermi liquid metal are:
  • the resistivity is quadratic in temperature at low temperatures.
  • the one-electron Green function has a simple pole in the complex energy plane. The strength of this pole is  the quasi-particle weight Z. 
The second is the more fundamental because it is connected with the existence of quasi-particles.

There are now a diverse range of strongly correlated electron materials which do not have the first signature. In particular, many have  a resistivity which is linear in temperature over a wide temperature range. However, this does not necessarily imply the absence of quasi-particles. For an illustration of some of the subtleties involved see this post.
In marginal Fermi liquid theory the scattering rate is linear in temperature but there is a non-zero quasi-particle weight, except at zero temperature.

As discussed in another post, Jan Zaanen claims that when the scattering rate (hbar/tau) has magnitude k_B T, one reaches the "Planckian limit" and there are no quasi-particles. It is not clear to me what is the basis of this claim. I welcome comments.


  1. Could you upload the Graph for its Wave function vs k (momentum) in 1D case for any simple model.

  2. and also for its Wave function vs x(position).