Tunneling through bilayer heterostructures: Two-point interactions

Abstract

A bilayer heterostructure is studied in the limit when the layers are squeezed to zero thickness and the distance between layers is fixed. Two-point interactions are realized for the cases: barrier-barrier, barrier-well, well-barrier, and well-well. While the barrier-barrier structure leads to the standard δ(x)–δ(x) interaction, where both Dirac’s delta functions are of the same positive polarity, the point approximation of the barrier-well structure is proven to be more singular than the δ(x) function. The realized point interactions are shown to be neither a sum of δ(x) and –δ(x) nor δ′(x). On the basis of a simple model with a rectangular well, a correct point approximation for the barrier-well structure is proposed.