Green function theory of virtual surface states

The method of factorisation is used to obtain a surface Green function to study the virtual surface states which arise when a linear field is applied to the surface of a nearly-free-electron crystal. Such an approach enables the normalisation problem encountered in previous treatments to be avoided. For a given surface termination, it is found that, although the surface-state energy depends on the gradient of the linear field, its actual location in the energy gap is governed by a 'competitive balance that is struck between the field gradient and the crystal surface potential. A singularity is found in the real part of the inverse surface Green function, which results in the surface-state energy being confined to a certain region of the energy gap, the actual region depending on the value of the surface termination parameter. A density-of-states calculation was performed to show the influence of the applied field on the position and lifetime of the virtual surface state.