Application of the multiband $kp$-models to quantum transport in quasi-periodic crystals

Abstract

We consider the quantum transport of a particle in a crystal where the global three-dimensional translation symmetry is removed. Our analysis concerns solid state structures where the microscopic potential of the ions is no longer periodic. This includes materials with variable chemical composition, intergrowth compounds and abrupt junctions. The application of the kp multiband envelope function models to the description of the quantum mechanical motion in such a quasi-periodic structure is investigated. By using a spectral decomposition technique, we show that when the interatomic distance is asymptotically small, the particle probability density can be obtained by the envelope kp model with variable coefficients.