Effect of disorder on a Pomeranchuk instability

TL;DR

This paper investigates how disorder affects the transition temperature of a Pomeranchuk instability, revealing similarities to d-wave superconductors and proposing disorder dependence as an indicator of Fermi surface distortions.

Contribution

It applies replica mean field theory to analyze disorder effects on Pomeranchuk instabilities, specifically for d-wave Fermi surface distortions, highlighting the disorder dependence of transition temperature.

Findings

Disorder reduces the transition temperature similarly to d-wave superconductors.

The transition remains second order in the studied regime.

Disorder dependence can serve as an indicator of Fermi surface distortions.

Abstract

We study the effect of disorder on the order parameter equation and transition temperature of a Pomeranchuk-type Fermi-surface instability using replica mean field theory. We consider the example of a phase transition to a $d_{x^2 +y^2}$ type Fermi surface distortion, and show that, in the regime where such a transition is second order, the transition temperature is reduced by disorder in essentially the same way as that for a d-wave superconductor. We argue that observing this disorder dependence of metal-to-metal transition might be a useful indicator of a finite angular momentum Fermi surface distortion.