Calculation of electronic surface states in superlattices via graph formulations

We propose a graph method for the analysis of electronic surface states in a complex basis superlattice terminated by surface with a multilayer clad. Using topology theory, we frame an energy equation for calculating the surface modes based on a graph model. Compared to the traditional methods, the present method does not have the problem of numerical instability for finding out the surface states of the superlattices. The other advantage is that the localized states are directly solved by the present method without spurious solutions, which usually exist in the solutions obtained by traditional methods. Numerical examples show removal of the spurious solutions by traditional methods may cause numerically instable and incorrect results.