Quenched disorder at antiferromagnetic quantum critical points in $2d$ metals

TL;DR

This paper investigates how quenched disorder affects antiferromagnetic quantum critical points in 2D metals, revealing that disorder destabilizes the non-Fermi liquid state and likely leads to Anderson localization at low energies.

Contribution

It provides a perturbative renormalization group analysis showing the instability of the clean non-Fermi liquid fixed point due to disorder in 2D SDW quantum critical metals.

Findings

Disorder destabilizes the non-Fermi liquid fixed point.

Flow towards strong coupling indicates disorder dominance.

Ground state likely becomes Anderson-localized at low energies.

Abstract

We study spin density wave quantum critical points in two dimensional metals with a quenched disorder potential coupling to the electron density. Adopting an $\epsilon$-expansion around three spatial dimensions, where both disorder and the Yukawa-type interaction between electrons and bosonic order parameter fluctuations are marginal, we present a perturbative, one-loop renormalization group analysis of this problem, where the interplay between fermionic and bosonic excitations is fully incorporated. Considering two different Gaussian disorder models restricted to small-angle scattering, we show that the non-Fermi liquid fixed point of the clean SDW hot-spot model is generically unstable and the theory flows to strong coupling due to a mutual enhancement of interactions and disorder. We study properties of the asymptotic flow towards strong coupling, where our perturbative approach eventually breaks down. Our results indicate that disorder dominates at low energies, suggesting that the ground-state in two dimensions is Anderson-localized.