# Effects of random potentials in three-dimensional quantum electrodynamics

## TL;DR

This paper investigates how different types of random potentials influence the low-energy behavior of massless Dirac fermions in three-dimensional quantum electrodynamics, revealing the dominant role of random scalar potentials in phase transitions.

## Contribution

It provides a detailed renormalization group analysis of the effects of random potentials, highlighting the enhanced impact of random mass and the dominance of scalar potentials in phase transitions.

## Key findings

- Random mass effects are significantly enhanced by gauge interactions.
- Random scalar and vector potentials are unaffected by gauge interactions at one-loop order.
- Random scalar potential induces a quantum phase transition.

## Abstract

Three-dimensional quantum electrodynamics exhibits a number of interesting properties, such as dynamical chiral symmetry breaking, weak confinement, and non-Fermi liquid behavior, and also has wide applications in condensed matter physics. We study the effects of random potentials, which exist in almost all realistic condensed-matter systems, on the low-energy behaviors of massless Dirac fermions by means of renormalization group method, and show that the role of random mass is significantly enhanced by the gauge interaction, whereas random scalar and vector potentials are insusceptible to the gauge interaction at the one-loop order. The static random potential breaks the Lorentz invariance, and as such induces unusual renormalization of fermion velocity. We then consider the case in which three types of random potentials coexist in the system. The random scalar potential is found to play a dominant role in the low-energy region, and drives the system to undergo a quantum phase transition.