  Inspired by the extension of the Standard Model, we analyzed the effects of
the spacetime anisotropies on a massive Dirac field through a non-minimal
CPT-odd coupling in the Dirac equation, where we proposed a possible scenario
that characterizes the breaking of the Lorentz symmetry which is governed by a
background vector field and induces a Landau-type quantization. Then, in order
to generalize our system, we introduce a hard-wall potential and, for a
particular case, we determine the energy levels in this background. In
addition, at the non-relativistic limit of the system, we investigate the
effects of the Lorentz symmetry violation on thermodynamic aspects of the
system.
