# Two dimensional metallic phases from disordered QED$_3$

## TL;DR

This paper demonstrates that (2+1)D QED with many fermion flavors can host stable metallic phases at zero temperature, stabilized by gauge fluctuations and disorder effects, explaining experimental 2D metallic behavior.

## Contribution

It establishes a stability criterion for disordered, strongly interacting Dirac fermions in 2D and shows that QED$_3$ can sustain metallic phases under weak disorder.

## Key findings

- QED$_3$ with many flavors remains metallic under weak scalar potential disorder.
- Weak mass disorder in QED$_3$ leads to a stable dirty metallic phase.
- Gauge fluctuations dynamically screen disorder, stabilizing metallic behavior.

## Abstract

Metallic phases have been observed in several disordered two dimensional (2d) systems, including thin films near superconductor-insulator transitions and quantum Hall systems near plateau transitions. The existence of 2d metallic phases at zero temperature generally requires an interplay of disorder and interaction effects. Consequently, experimental observations of 2d metallic behavior have largely defied explanation. We formulate a general stability criterion for strongly interacting, massless Dirac fermions against disorder, which describe metallic ground states with vanishing density of states. We show that (2+1)-dimensional quantum electrodynamics (QED$_3$) with a large, even number of fermion flavors remains metallic in the presence of weak scalar potential disorder due to the dynamic screening of disorder by gauge fluctuations. We also show that QED$_3$ with weak mass disorder exhibits a stable, dirty metallic phase in which both interactions and disorder play important roles.