Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals

TL;DR

This paper investigates the stability and quantum critical behavior of three-dimensional Dirac semimetals under interactions and disorder, revealing distinct Gaussian and non-Gaussian critical points and their stability conditions.

Contribution

It classifies quantum critical points in dirty Dirac semimetals, showing the stability of certain fixed points and the emergence of a multicritical point from their interplay.

Findings

Interaction-driven critical points are Gaussian and mean-field in nature.

Disorder-driven critical points are non-Gaussian and describe metallic transitions.

Two stable quantum critical points exist in the presence of chiral symmetric disorder.

Abstract

We theoretically study the stability of three dimensional Dirac semimetals against short-range electron-electron interaction and quenched time-reversal symmetric disorder (but excluding mass disorder). First we focus on the clean interacting and the noninteracting dirty Dirac semimetal separately, and show that they support two distinct quantum critical points. Using renormalization group techniques, we find that while interaction driven quantum critical points are \emph{Gaussian} (mean-field) in nature, describing quantum phase transitions into various broken symmetry phases, the ones controlled by disorder are \emph{non-Gaussian}, capturing the transition to a metallic phase. We classify such diffusive quantum critical points based on the transformation of disorder vertices under a \emph{continuous} chiral rotation. Our wek coupling renormalization group analysis suggests that two distinct quantum critical points are stable in an interacting dirty Dirac semimetal (with chiral symmetric randomness), and a multicritical point (at finite interaction and disorder) results from their interplay. By contrast, the chiral symmetry breaking disorder driven critical point is unstable against weak interactions. Effects of weak disorder on the ordering tendencies in Dirac semimetal are analyzed. The clean interacting critical points, however, satisfy the \emph{Harris criterion}, and are therefore expected to be unstable against bond disorder. Although our weak coupling analysis is inadequate to establish the ultimate stability of these fixed points in the strong coupling regime (when both interaction and disorder are strong), they can still govern crossover behaviors in Dirac semimetals over a large length scale, when either interaction or randomness is sufficiently weak.