Analytic solution for Gauged Dirac-Weyl equation in $(2+1)$-dimensions

TL;DR

This paper derives exact self-dual solutions for a gauged Dirac-Weyl equation in (2+1) dimensions, relevant for graphene physics, especially when coupled with Chern-Simons gauge fields, revealing parallels with nonrelativistic models.

Contribution

It provides the first analytic self-dual solutions for the gauged Dirac-Weyl equation in (2+1) dimensions with Chern-Simons interaction.

Findings

Exact self-dual solutions are obtained.

Solutions match those of nonrelativistic Chern-Simons matter systems.

Highlights the relevance for graphene and topological field theories.

Abstract

A gauged Dirac-Weyl equation in (2+1)-dimension is considered. This equation has the particularity to describe the states of a graphene Dirac matter. In particular we are interested in matter interacting with a Chern-Simons gauge fields. We show that exact self-dual solutions are admitted. These solutions are the same as those supported by nonrelativistic matter interacting with a Chern-Simons gauge field.