Energy levels of an electron in a circular quantum dot in the presence of spin-orbit interactions

V. V. Kudryashov,A. V. Baran

doi:10.35596/1729-7648-2021-19-8-20-25

V. V. Kudryashov, A. V. Baran

Open Access

https://doi.org/10.35596/1729-7648-2021-19-8-20-25

Copy DOI

Journal: Doklady BGUIR	Publication Date: Jan 2, 2022
Citations: 1	License type: cc-by

Affiliation: B.I. Stepanov Institute of Physics

Abstract

The two-dimensional circular quantum dot in a double semiconductor heterostructure is simulated by a new axially symmetric smooth potential of finite depth and width. The presence of additional potential parameters in this model allows us to describe the individual properties of different kinds of quantum dots. The influence of the Rashba and Dresselhaus spin-orbit interactions on electron states in quantum dot is investigated. The total Hamiltonian of the problem is written as a sum of unperturbed part and perturbation. First, the exact solution of the unperturbed Schrödinger equation was constructed. Each energy level of the unperturbed Hamiltonian was doubly degenerated. Further, the analytical approximate expression for energy splitting was obtained within the framework of perturbation theory, when the strengths of two spin-orbit interactions are close. The numerical results show the dependence of energy levels on potential parameters.

Highlights

The motion of an electron in an inner layer of a double semiconductor heterostructure is usually treated as two-dimensional in the (x, y) plane
The presence of additional potential parameters in this model allows us to describe the individual properties of different kinds of quantum dots
It can be experimentally achieved due to the fact that the Rashba interaction strength can be controlled by an external electric field, and the Dresselhaus interaction strength can be varied by changing the width of quantum well along the z axis [3, 7]

Summary

Introduction

The motion of an electron in an inner layer of a double semiconductor heterostructure is usually treated as two-dimensional in the (x, y) plane. The planar motion is restricted if an electron is placed in a quantum dot localized in the middle layer of heterostructure. The Rashba VR [1] and Dresselhaus VD [2] interactions are presented by the formulas. D achieved due to the fact that the Rashba interaction strength can be controlled by an external electric field, and the Dresselhaus interaction strength can be varied by changing the width of quantum well along the z axis [3, 7]

Methods and results

Conclusion