Point interactions with bias potentials

Alexander V. Zolotaryuk, Georgios Tsironis, Yaroslav Zolotaryuk

Research output: Contribution to journalArticle

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.

Original languageEnglish
Article number87
JournalFrontiers in Physics
Volume7
Issue numberJUN
DOIs
Publication statusPublished - Jan 1 2019

Fingerprint

Point Interactions
Semiconductors
Physics
Equipment and Supplies
Heterostructures
Heterojunctions
Transistors
interactions
transistors
matrices
Voltage
Electric potential
Wave functions
asymptotic methods
Asymptotic Methods
electric potential
Wave Function
External Field
Boundary conditions
Biased

Keywords

  • Controllable potentials
  • Heterostructures
  • One-dimensional quantum systems
  • Point interactions
  • Resonant tunneling
  • Transmission

ASJC Scopus subject areas

  • Biophysics
  • Materials Science (miscellaneous)
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

Zolotaryuk, A. V., Tsironis, G., & Zolotaryuk, Y. (2019). Point interactions with bias potentials. Frontiers in Physics, 7(JUN), [87]. https://doi.org/10.3389/fphy.2019.00087

Point interactions with bias potentials. / Zolotaryuk, Alexander V.; Tsironis, Georgios; Zolotaryuk, Yaroslav.

In: Frontiers in Physics, Vol. 7, No. JUN, 87, 01.01.2019.

Research output: Contribution to journalArticle

Zolotaryuk, AV, Tsironis, G & Zolotaryuk, Y 2019, 'Point interactions with bias potentials', Frontiers in Physics, vol. 7, no. JUN, 87. https://doi.org/10.3389/fphy.2019.00087
Zolotaryuk AV, Tsironis G, Zolotaryuk Y. Point interactions with bias potentials. Frontiers in Physics. 2019 Jan 1;7(JUN). 87. https://doi.org/10.3389/fphy.2019.00087
Zolotaryuk, Alexander V. ; Tsironis, Georgios ; Zolotaryuk, Yaroslav. / Point interactions with bias potentials. In: Frontiers in Physics. 2019 ; Vol. 7, No. JUN.
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