Jure Kokalj and I have just finished a paper Consistent description of the metallic phase of overdoped cuprate superconductors as an anisotropic marginal Fermi liquid
We consider a model electronic self energy, motivated by Angle-Dependent Magneto-Resistance (ADMR) experiments, and consisting of two terms:
The first term has the frequency and temperature dependence of a Fermi liquid (FL) and is isotropic on the Fermi surface.
The second term has the same frequency and temperature dependence as that of a Marginal Fermi liquid, [but in contrast to the original form proposed by Varma et al.] is anisotropic over the Fermi surface, and vanishes in the same directions as the superconducting gap and the pseudogap observed in underdoped cuprates.This model self energy gives a consistent description of results from ADMR, specific heat, de Haas van Alphen, and ARPES experiments. In particular, we have reconciled a strongly doping dependent anomalous scattering rate observed in ADMR with an almost doping independent specific heat. This was a question originally posed to us by Nigel Hussey and which I discussed in an earlier post, A key property of cuprate superconductors.
Although the scattering can be dominated by the anisotropic Marginal Fermi liquid term the quasi-particle renormalization is dominated by the FL term.
We also show that several predictions of the Hidden Fermi liquid (HFL) theory (proposed by Anderson and Casey) is inconsistent with the observed temperature and doping dependence of the scattering rate and with the magnitude of the specific heat.
The figure below shows the doping dependence of the density of states at the Fermi energy (which is a measure of the quasi-particle renormalisation) that is implied by the form of the imaginary part of the self energy required by the results of ADMR experiments.