On the Normal State of the High Temperature Superconductors

TL;DR

This paper uses a Fermi liquid model to analytically and numerically explain the linear temperature resistivity and optical conductivity in high-temperature cuprate superconductors, emphasizing the role of van-Hove singularities.

Contribution

It demonstrates that strong peaks in the density of states near the chemical potential can account for observed normal state properties of cuprates, supported by numerical calculations.

Findings

Linear in temperature resistivity explained

Optical conductivity linear in 1/energy derived

Van-Hove singularities pinned near chemical potential

Abstract

Based on a Fermi liquid model, we present several results on the normal state of the optimally doped and overdoped cuprate superconductors. Our main result is an analytic demonstration, backed by self-consistent numerical calculations, of the linear in temperature resistivity and linear in 1/(energy) optical conductivity, provided the interacting Fermi liquid has strong peaks in its density of states (van-Hove singularities in 2 dimensions) near the chemical potential. Moreover, we find that the interactions tend to pin these strong peaks close to the chemical potential. This fact compares favorably with experiment on a variety of cuprates. Finally, we show that the above scenario yields naturally the low energy dependence of the experimentally determined susceptibility, without reference to spin waves.