Calculations of exchange interaction in impurity band of two-dimensional semiconductors with out of plane impurities

TL;DR

This paper investigates the exchange interaction between two electrons in a two-dimensional semiconductor with out-of-plane impurities, deriving analytical formulas for singlet-triplet splitting across various impurity configurations.

Contribution

It introduces a novel analysis of impurity-induced exchange interactions in 2D semiconductors with out-of-plane impurities, adapting methods from atomic physics.

Findings

Analytical expressions for singlet-triplet splitting in different impurity configurations.

The splitting's dependence on impurity distances weakens as vertical distances increase.

Interpolated formulas for intermediate impurity arrangements are provided.

Abstract

We calculate the singlet-triplet splitting for a couple of two-dimensional electrons in the potential of two positively charged impurities which are located out of plane. We consider different relations between vertical distances of impurities $h_1$ and $h_2$ and their lateral distance $R$. Such a system has never been studied in atomic physics but the methods, worked out for regular two-atomic molecules and helium atom, have been found to be useful. Analytical expressions for several different limiting configurations of impurities are obtained an interpolated formula for intermediate range of parameters is proposed. The $R$-dependence of the splitting is shown to become weaker with increasing $h_1,h_2$.