A relativistic green matrix method to calculate the surface states in a semi-infinite three-dimensional crystal

In this paper, we develop a relativistic Green matrix method in the Dirac formalism, which can be considered as ageneralization of the non relativistic Green function method of Scherer and Phariseau to calculate the surface states in a semi-infinite three-dimensional crystal. For simplicity, only the case of one atom in a unit cell is considered. The wave vectors for spin up and spin down are assumed to be different. We demostrate the existence of a two-dimensional relativistic bandstructure localized at the surface. We also discuss the possibility of obtaining the three-dimensional relativistic bulkbandstructure as a special case of our theory.