Interaction effects on 2D fermions with random hopping

TL;DR

This paper investigates how short-range interactions affect 2D Dirac fermions with chiral disorder, revealing that disorder can induce strong relevance of interactions, leading to instability unlike the stable clean system.

Contribution

It demonstrates, via renormalization group analysis, that disorder can cause interactions to become relevant in 2D Dirac fermions, unlike in the clean case.

Findings

Disorder induces a divergence in the density of states.

Interactions become strongly relevant due to disorder.

Clean Dirac fermions are stable against weak interactions.

Abstract

We study the effects of generic short-ranged interactions on a system of 2D Dirac fermions subject to a special kind of static disorder, often referred to as ``chiral.'' The non-interacting system is a member of the disorder class BDI [M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)]. It emerges, for example, as a low-energy description of a time-reversal invariant tight-binding model of spinless fermions on a honeycomb lattice, subject to random hopping, and possessing particle-hole symmetry. It is known that, in the absence of interactions, this disordered system is special in that it does not localize in 2D, but possesses extended states and a finite conductivity at zero energy, as well as a strongly divergent low-energy density of states. In the context of the hopping model, the short-range interactions that we consider are particle-hole symmetric density-density interactions. Using a perturbative one-loop renormalization group analysis, we show that the same mechanism responsible for the divergence of the density of states in the non-interacting system leads to an instability, in which the interactions are driven strongly relevant by the disorder. This result should be contrasted with the limit of clean Dirac fermions in 2D, which is stable against the inclusion of weak short-ranged interactions. Our work suggests a novel mechanism wherein a clean system, initially insensitive to interaction effects, can be made unstable to interactions upon the inclusion of weak static disorder.