A new method in the quantum theory of surface states

Abstract

The theory of states at surfaces and interfaces is formulated applying the equivalent potential method previously used in the analysis of pseudopotentials. The surface boundary conditions are replaced by an equivalent `perturbation' localized at the surface, which exactly conserves scattering amplitudes and energy eigenvalues. For an abrupt discontinuity at an interface between two media, A and B, a central formula is obtained which factorizes the surface Green function. The factors involved depend only on the surface values of GA and GB, these being the Green functions of the corresponding medium continued into the entire space. This yields a completely new secular equation for the energies of the surface states, which avoids the need to do a complex band structure calculation. The method can also be used to study surface scattering (e.g. LEED theory) as well as surface impurities.