Charge and Spin Currents in a Lower-Dimensional Supersymmetric Model in Presence of Vortices

TL;DR

This paper explores charge and spin currents in a (2+1)-dimensional supersymmetric field theory with vortices, analyzing symmetry breaking, fermionic spectra, and potential implications for materials like graphene and topological insulators.

Contribution

It introduces a supersymmetric model with Chern-Simons term and non-minimal couplings, examining vortex effects and SUSY breaking in lower-dimensional systems.

Findings

Identification of charge and spin currents in the model

Derivation of fermionic mass gap related to model parameters

Insights into SUSY's role in material properties

Abstract

We investigate charge and spin currents that may appear in some materials, considering the possible couplings and the symmetries of a field-theoretical model presented here. We inspect these possible currents in (1+2) dimensions by adopting an N =2 - D=3 supersymmetric framework with a Chern-Simons term and non-minimal couplings as well. We discuss a number of aspects in connection with a vortex configuration that is topologically viable. The new features of our investigation take into account the nature of both the U(1)-symmetry and supersymmetry (SUSY) breakings in presence of the vortex. We focus on aspects of the fermionic sector and their interactions with the currents. In connection with the spectrum of fermions, we also derive the mass gap in terms of the parameters of the the model. Another point we highlight is the role SUSY in our considerations. Once graphene and topological insulator materials are described by a Dirac-like equation, we assume, as a working hypothesis, that SUSY may also have some influence on the properties of these materials. Along this line, it is mandatory to connect the SUSY breakdown to this class of materials. We believe that our discussion could bring some elements for the understanding of this category of lower-dimensional systems.