On the influence of a Chern-Simons term in the dynamical fermion masses in Reduced or Pseudo QED

Mixed dimensional theories have been used to describe condensed matter systems where fermions are constrained to a plane while the gauge fields they interact with remain four-dimensional. Here we investigate dynamical breaking of chiral symmetry in the framework of a mixed-dimensional theory that has been successful in describing graphene and other planar Dirac materials and has been dubbed as Pseudo or Reduced Quantum Electrodynamics. We explore the interplay between the gauge and fermion sector when a Chern-Simons term is considered and, by exploring the tensor structure of the fermion self energy, we show that the radiative corrections may induce both, a Dirac and a Haldane mass term. Furthermore, by solving the corresponding Schwinger-Dyson equation in a suitable truncation, we explore non-perturbatively the dynamical generation of fermion masses for different values of the electromagnetic coupling and the Chern-Simons coefficient. We also show that for definite parameter values, the contributions from each chirality cancel out and the chiral symmetry may be restored. Possible implications of this result for physical systems, in particular on what concerns the chiral magnetic effect, are discussed.