Superlattices with coupled channels and transfer matrices

Abstract

We study analytically threshold and resonance effects in superlattices using the well-known transfer matrix technique. For this analysis we take advantage of a new parametrization of the scattering amplitudes. In particular, threshold effects, analogous to the so-called “Wigner cusps” of nuclear reactions, follow when a channel is opened for non-zero coupling. Sharp resonances of Lorenzian shape are also found only in the presence of coupling. It could be very interesting to look for experimental evidences of these effects. We expect that this approach allows to study systems with spin and under external magnetic fields.