Disorder effects at a nematic quantum critical point in d-wave cuprate superconductor

TL;DR

This paper investigates how different types of disorder affect the nematic quantum critical point in a d-wave cuprate superconductor, revealing that some disorders are irrelevant while others destabilize the transition.

Contribution

It provides a detailed renormalization group analysis showing the impact of various disorder types on the stability of the nematic quantum critical point.

Findings

Random mass and gauge field disorders are irrelevant and do not alter the fixed point.

Random chemical potential disorder destabilizes the nematic phase transition.

The study clarifies the role of disorder in the quantum critical behavior of cuprate superconductors.

Abstract

A d-wave high temperature cuprate superconductor exhibits a nematic ordering transition at zero temperature. Near the quantum critical point, the coupling between gapless nodal quasiparticles and nematic order parameter fluctuation can result in unusual behaviors, such as extreme anisotropy of fermion velocities. We study the disorder effect on the nematic quantum critical behavior and especially on the flow of fermion velocities. The disorders that couple to nodal quasiparticles are divided into three types: random mass, random gauge field, and random chemical potential. A renormalization group analysis shows that random mass and random gauge field are both irrelevant and thus do not change the fixed point of extreme velocity anisotropy. However, the marginal interaction due to random chemical potential destroys this fixed point and makes the nematic phase transition unstable.