  The paper deals with the semi-Dirac operator in a half-space arising in the
description of quasiparticles in quantum mechanics as well as in semi-metals
materials and related structures. It completely shows the self-adjointness,
computes the square and the spectrum of the operator. We also set up sufficient
conditions for the existence of the point and discrete spectrum by including
some appropriate potentials in the problem and study the spectral stability
properties for perturbed operators.
