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

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.