Competition between excitonic gap generation and disorder scattering in graphene

TL;DR

This paper investigates how disorder affects excitonic gap formation in graphene, revealing a phase transition driven by the competition between Coulomb interactions and disorder scattering, with no coexistence of gap and scattering.

Contribution

It provides a self-consistent analysis of the interplay between excitonic gap generation and disorder scattering in graphene, identifying a phase diagram with a critical line separating insulating and metallic phases.

Findings

Existence of a critical line dividing phases with and without excitonic gap

No coexistence of finite gap and scattering rate

Disorder can induce a quantum phase transition from insulator to metal

Abstract

We study the disorder effect on the excitonic gap generation caused by strong Coulomb interaction in graphene. By solving the self-consistently coupled equations of dynamical fermion gap $m$ and disorder scattering rate $\Gamma$, we found a critical line on the plane of interaction strength $\lambda$ and disorder strength $g$. The phase diagram is divided into two regions: in the region with large $\lambda$ and small $g$, $m \neq 0$ and $\Gamma = 0$; in the other region, $m = 0$ and $\Gamma \neq 0$ for nonzero $g$. In particular, there is no coexistence of finite fermion gap and finite scattering rate. These results imply a strong competition between excitonic gap generation and disorder scattering. This conclusion does not change when an additional contact four-fermion interaction is included. For sufficiently large $\lambda$, the growing disorder may drive a quantum phase transition from an excitonic insulator to a metal.