Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation

TL;DR

This paper uses bosonisation to analyze interacting Dirac fermions on boundaries of 3D topological crystalline insulators, revealing a variety of topologically massive gauge theories including extended Chern-Simons models.

Contribution

It introduces a formalism employing bosonisation to describe interacting boundary fermions of 3D topological crystalline insulators via diverse topological gauge theories.

Findings

Derivation of effective topologically massive gauge theories from fermion interactions.

Identification of extended Chern-Simons theories with higher derivatives.

Framework applicable to gapped boundaries of 3D topological crystalline insulators.

Abstract

Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion interactions the system can be effectively described by a rich variety of topologically massive gauge theories. Among these effective theories, we obtain an extended Chern-Simons theory with higher order derivatives as well as two coupled Chern-Simons theories. Our formalism allows for a general description of interacting fermions emerging, for example, at the gapped boundary of three-dimensional topological crystalline insulators.