Abstract
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 pseudo or reduced quantum electrodynamics. We explore the interplay between the gauge and fermion sectors 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 nonperturbatively explore 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.
Highlights
Quantum electrodynamics in two spatial and one temporal dimension (QED3) has been intensively studied in the past mainly because it shares two important features with quantum chromodynamics (QCD): chiral symmetry breaking (CSB) and confinement [1,2]
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 pseudo or reduced quantum electrodynamics
In a 1=N expansion for pure QED3, it has been shown that in most cases there is a critical number of fermion flavors, above which the chiral symmetry breaking is restored [3,5,6,27]
Summary
Quantum electrodynamics in two spatial and one temporal dimension (QED3) has been intensively studied in the past mainly because it shares two important features with quantum chromodynamics (QCD): chiral symmetry breaking (CSB) and confinement [1,2]. In a 1=N expansion for pure QED3, it has been shown that in most cases there is a critical number of fermion flavors, above which the chiral symmetry breaking is restored [3,5,6,27] Beyond this approximation, refined vertices and vacuum polarization effects agree with these findings in general, refining the details of the critical line [17]. QED3 has been shown to correctly describe the charge carriers in Dirac materials, interactions between these electrons and external electromagnetic fields cannot be correctly described by the full-fledged dimensionally reduced theory including gauge fields in (2 þ 1) dimensions This is due to the fact that, the fermionic quasiparticles are constrained to the plane, the gauge fields live in a bulk of higher dimensions and it is necessary to consider a mixed-dimensional theory to correctly describe this interaction. IV we draw our conclusions and comment on possible implications of our results on high-energy-related condensed matter phenomena
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