A metal and an insulator at the same time?

Michael Smith brought to my attention a really nice preprint, Interplay charge dynamics in a valence-bond dynamical mean-field theory of cuprate superconductors, by Michel Ferrero, Olivier Parcollet, Gabriel Kotliar, and Antoine Georges.

This helps resolve the following major puzzle about the metallic state of the cuprate superconductors. In conventional metals (insulators) one observes that the resistivity monotonically increases (decreases) with increasing temperature. Indeed for currents parallel to layers the cuprates show the temperature dependence characteristic of a metal. But, for currents perpendicular to the layers underdoped systems show a temperature dependence characteristic of an insulator.

How can it be a metal in one direction and an insulator in another?

It turns out that the key physics involved is:

• the interlayer tunneling matrix element is momentum dependent (as required by the symmetry of the crystal) and vanishes in the parts of the Brillouin zone in which the nodes of the pseudogap occur in the underdoped system.
• this means that the interlayer charge dynamics is dominated by the antinodal region and so particularly sensitive to the pseudogap
• the temperature dependence of the scattering rate in the nodal region is sensitive to doping and at low temperatures the nodal quasi-particles become more coherent

Some of this physics was anticipated in a phenomenological "cold spots" model by Ioffe and Millis in 1998. What is new and important about Ferrero et al.'s work is that they start with a Hubbard model and calculate the temperature, frequency, and doping dependence that are consistent with experiment.

It is also interesting to me that rho* in the figure above has the value characteristic of a bad metal.