Conditions for perfect transmission of quantum particles across layered heterostructures and resonance effects of an auxiliary well potential

Abstract

We consider the bilayer heterostructure composed of the layer described by a rectangle-like potential and the background layer with an arbitrary potential profile given only by a transmission matrix. The conditions for the perfect (zero reflection) transmission of quantum particles across this structure is derived in the form of two basic equations on the rectangular layer parameters and the distance between the layers. The solution of these equations is analyzed in detail including some special cases and squeezing approximations. The effect of a rectangular well potential on the tunneling of particles with infinitesimally low energy through the background layer is investigated.