AUTHOR=Zolotaryuk Alexander V. , Tsironis Giorgos P. , Zolotaryuk Yaroslav TITLE=Point Interactions With Bias Potentials JOURNAL=Frontiers in Physics VOLUME=7 YEAR=2019 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00087 DOI=10.3389/fphy.2019.00087 ISSN=2296-424X ABSTRACT=

We develop an approach on how to define single-point interactions under the application of external fields. The essential feature relies on an asymptotic method based on the one-point approximation of multi-layered heterostructures that are subject to bias potentials. In this approach, the zero-thickness limit of the transmission matrices of specific structures is analyzed and shown to result in matrices connecting the two-sided boundary conditions of the wave function at the origin. The reflection and transmission amplitudes are computed in terms of these matrix elements as well as biased data. Several one-point interaction models of two- and three-terminal devices are elaborated. The typical transistor in the semiconductor physics is modeled in the “squeezed limit” as a δ- and a δ′-potential and referred to as a “point” transistor. The basic property of these one-point interaction models is the existence of several extremely sharp peaks as an applied voltage tunes, at which the transmission amplitude is non-zero, while beyond these resonance values, the heterostructure behaves as a fully reflecting wall. The location of these peaks referred to as a “resonance set” is shown to depend on both system parameters and applied voltages. An interesting effect of resonant transmission through a δ-like barrier under the presence of an adjacent well is observed. This transmission occurs at a countable set of the well depth values.