Exchange effects on electron scattering through a quantum dot embedded in a two-dimensional semiconductor structure

TL;DR

This paper introduces a theoretical approach to analyze electron scattering in a 2D semiconductor quantum dot, accounting for exchange interactions, and provides detailed cross-section calculations for elastic and inelastic processes.

Contribution

The paper develops a novel method combining continued fractions and partial-wave expansion to include exchange effects in electron scattering on quantum dots.

Findings

Calculated elastic and spin-flip scattering cross-sections for singlet and triplet states.

Demonstrated the method's applicability to inelastic scattering processes.

Provided insights into exchange effects in 2D quantum dot electron scattering.

Abstract

We have developed a theoretical method to study scattering processes of an incident electron through an N-electron quantum dot (QD) embedded in a two-dimensional (2D) semiconductor. The generalized Lippmann-Schwinger equations including the electron-electron exchange interaction in this system are solved for the continuum electron by using the method of continued fractions (MCF) combined with 2D partial-wave expansion technique. The method is applied to a one-electron QD case. Cross-sections are obtained for both the singlet and triplet couplings between the incident electron and the QD electron during the scattering. The total elastic cross-sections as well as the spin-flip scattering cross-sections resulting from the exchange potential are presented. Furthermore, inelastic scattering processes are also studied using a multichannel formalism of the MCF.