### 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 language | English |
---|---|

Article number | 87 |

Journal | Frontiers in Physics |

Volume | 7 |

Issue number | JUN |

DOIs | |

Publication status | Published - Jan 1 2019 |

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### 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

*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.

Research output: Contribution to journal › Article

*Frontiers in Physics*, vol. 7, no. JUN, 87. https://doi.org/10.3389/fphy.2019.00087

}

TY - JOUR

T1 - Point interactions with bias potentials

AU - Zolotaryuk, Alexander V.

AU - Tsironis, Georgios

AU - Zolotaryuk, Yaroslav

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Controllable potentials

KW - Heterostructures

KW - One-dimensional quantum systems

KW - Point interactions

KW - Resonant tunneling

KW - Transmission

UR - http://www.scopus.com/inward/record.url?scp=85068503919&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068503919&partnerID=8YFLogxK

U2 - 10.3389/fphy.2019.00087

DO - 10.3389/fphy.2019.00087

M3 - Article

VL - 7

JO - Frontiers in Physics

JF - Frontiers in Physics

SN - 2296-424X

IS - JUN

M1 - 87

ER -