Band theory of superlattices

We present a first-principles theory of the band structure of lattice-matched superlattices. We formulate the one-electron problem of superlattices in the Bloch representation of one of the constituent materials. In this formulation, the symmetry breaking along the superlattice axis leads to partitioning and folding of the original homogeneous crystal Brillouin zone onto a thin region around the center of the zone. A single homogeneous crystal Bloch function becomes a multicomponent wave function. Each component represents a superlattice subband. We use L\"owdin's theorem to derive series expressions for the subband energies and wave functions, and discuss the relation between these solutions and the eigenvalues and eigenfunctions corresponding to quantum-well models. We apply the general results to a superlattice composed of two different types of simple two-band model materials.