  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.
