Resonant behavior, symmetry, and singularity of the transfer matrix in asymmetric tunneling structures

Abstract

We investigate the energy dependence and symmetry properties of the transfer matrix describing the tunneling and reflection processes in multiple asymmetric localized potential barriers. In particular, we show that certain quasi-bound states result in Lorentzian peaks of the diagonal matrix element of the transfer matrix in the energy region where tunneling is impossible. The change of symmetry properties of the transfer matrix in this energy range is established and related to a characteristic behavior of the phase of the reflection amplitude. This analysis is verified using quasi-classical theory of asymmetric double barriers and numerical calculations of the transfer matrix in electrically biased finite superlattices.