Superlattices with coupled degenerated spectrum

Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana - Mexico City, C.P. 02200, Mexico

Received: 27 January 2016
Accepted: 7 April 2016

Abstract

Two new analytical results are given which are of great help to understand superlattices with coupled modes. The first is an explicit relation for the transfer matrices in terms of Schur functions and Chebyshev polynomials. The second is a condition which generalizes the old well-known Floquet-Bloch trace condition to determine the spectrum. These improvements allow a fast computation of scattering amplitudes without obscuring the calculation with complicated numerical methods. As the energy grows, the eigenvalues degeneracy determines two types of transmission gaps. It is shown that these results could make it possible to design in greater detail the energy spectrum, for the very interesting case including modes coupling and degeneracy. They keep the understanding on the same footing as that of the traditional basic uncoupled problem considered at the beginning of the study of superlattices, like the Kroning-Penning model, or by Floquet-Bloch's theorem, or later by Esaki for heterostructures.