Surface States in a Square Lattice under Magnetic Field Applied in the Surface Region

Electronic surface states localized on the edge of a semi-inflnite square lattice are studied in the tight binding approximation. We examined the existence of surface states in the presence of magnetic fleld applied in the surface region of a 2D lattice. The applied fleld is perpendicular to the lattice and conflned to a stripe near the surface. We also included a surface site perturbation caused by the presence of the surface. The magnetic fleld is introduced into the model by the Peierls substitution.