Effects of a Landau-type quantization induced by the Lorentz symmetry violation on a Dirac field

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.