Spectral properties of two-dimensional half-space semi-Dirac semi-metals

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.