Relativistic surface states in the presence of an impurity and a distortion at the surface

Abstract

Using an approach due to Steslicka and Davison, we have investigated relativistically the field-free surface states of a one-dimensional (semi-infinite) system, with simultaneous presence of an impurity and a distortion at the surface. The bulk potentials are taken as δ-wells (attractive) and the impurity potential is represented by δ-barriers (repulsive). The relativistic surface state energies are computed as functions of the vacuum potential discontinuity, for various sets of parameters, and their locations in the band gaps are indicated. The relativistic results are compared with those corresponding to the non-relativistic treatment of the same model, and the circumstances under which the relativistic results would be significantly different from the non-relativistic ones are examined critically. It is found that the difference between the relativistic and non-relativistic results depends, in general, substantially on the strengths of the bulk and impurity potentials as well as the extent of the surface distortion.