Monday, May 5, 2014

Is there a Fermi liquid associated with the pseudogap state of the cuprates?

To me this seems at first to be a strange idea. The phenomenology of the cuprates and doped Hubbard models is roughly that as the doping decreases one goes from a Fermi liquid (large overdoping with no superconductivity) to an anisotropic marginal Fermi liquid  (overdoped but superconducting) to strange metal (marginal Fermi liquid) (optimal doping) to pseudogap state (underdoping). Hence, I would have thought that everything was rather non-Fermi liquid like in the pseudogap state.

However, the observation in the pseudogap range of copings of quantum magnetic oscillations (that could be associated with a small Fermi surface) and Fermi arcs, raised the question of a Fermi liquid state.

Over the past few years Martin Greven and collaborators have performed a range of transport measurements on a relatively clean single layer cuprate material Hg1201. They find Fermi liquid type behaviour [e.g. resistivity quadratic in temperature, scattering rates quadratic in frequency] for a range of temperatures below the pseudogap temperature T*.

A recent preprint is
Validity of Kohler's rule in the pseudogap phase of the cuprate superconductors
M. K. Chan, M. J. Veit, C. J. Dorow, Y. Ge, Y. Li, W. Tabis, Y. Tang, X. Zhao, N. Barišić, M. Greven

What is Kohler's rule?

In simple metals the temperature and magnetic field dependence of the magnetoresistance is dominated by the orbital motion of the electrons and described by some function of the product of omega_c and tau.

omega_c is the cyclotron frequency which is proportional to the magnetic field B and independent of temperature.
tau is the scattering time, which is temperature dependent and field independent, and should have the same temperature dependence as 1/rho where rho(B=0) is the resistivity in zero field.

These observations lead to Kohler's rule which is obeyed by simple metals.
A plot of the ratio of the rho(B)/rho(B=0) versus B/rho(B=0) should be independent of temperature.

In 1995 Ong's group observed significant violations of Kohler's rule in the underdoped and overdoped cuprates. Similar results were found by a Japanese group.

In 1998 I pointed out that in one mysterious organic metal there were also significant violations. The paper also has an extensive discussion of reasons why Kohler's rule can fail.

In the preprint, the authors find results consistent with Kohler's rule for Hg2201 samples with Tc=70 K and 81K, and temperatures between about 100 K and 200 K, and fields up to 30 Tesla.
The left plot is the bare data and the right plot is the data rescaled according to Kohler's rule.

Is the idea of Fermi liquid in the pseudogap region reasonable?
The scenario may be something like this.
There are Fermi liquid like quasi-particles near the nodes of the pseudogap. The non-Fermi liquid excitations occur towards the anti-nodal regions. This is the basic idea of the anisotropic marginal Fermi liquid developed for overdoped cuprates. Suppose one assumes something like that model actually applies for all doping. Then in the pseudogap region the non-Fermi liquid part will start to get gapped out and one will just be left with the Fermi liquid part. This can then undergo charge ordering instabilities to form Fermi surface pockets due to Fermi surface reconstruction.

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