Evaluation of Surface-State Theories

Fundamentals of surface-state theory, such as analytic continuation and limitations of the Bloch theorem in a finite lattice, are critically discussed. For illustrative purposes, a specific and simple surface-state problem is then solved by different methods: the coefficient method, the scattering method, the determinant method, and the integral method. Many novel points of view and interconnections are introduced. The advantages and disadvantages of each method are stressed, especially with respect to more complicated problems such as three-dimensional surface states on zinc blende.