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

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.