Disordered fermionic quantum critical points

TL;DR

This paper investigates how quenched disorder influences the quantum phase transition in a 2D Dirac semimetal, revealing a transition from clean to disordered critical behavior with unique critical exponents and oscillatory scaling for higher fermion flavors.

Contribution

It introduces a perturbative RG analysis of disordered fermionic quantum critical points, identifying new finite-disorder fixed points and their properties for various fermion flavor numbers.

Findings

Disorder induces a new finite-disorder critical point for N≥2.

Critical exponents become non-Gaussian and dynamic exponent z>1 at the disordered fixed point.

For N≥7, the fixed point exhibits stable-focus behavior with oscillatory corrections to scaling.

Abstract

We study the effect of quenched disorder on the semimetal-superconductor quantum phase transition in a model of two-dimensional Dirac semimetal with $N$ flavors of two-component Dirac fermions, using perturbative renormalization group methods at one-loop order in a double epsilon expansion. For $N\geq 2$ we find that the Harris-stable clean critical behavior gives way, past a certain critical disorder strength, to a finite-disorder critical point characterized by non-Gaussian critical exponents, a noninteger dynamic critical exponent $z>1$, and a finite Yukawa coupling between Dirac fermions and bosonic order parameter fluctuations. For $N\geq 7$ the disordered quantum critical point is described by a renormalization group fixed point of stable-focus type and exhibits oscillatory corrections to scaling.