Self-consistent approach for excitons in quantum wells

TL;DR

This paper presents a new self-consistent computational method for calculating exciton properties in quantum wells, simplifying the process while maintaining accuracy, especially for shallow wells.

Contribution

A novel self-consistent approach that separates motion directions and provides analytical expressions for shallow wells, reducing computational effort.

Findings

Excellent agreement with variational calculations.

Analytical expression for exciton binding energy.

Reduced computational complexity.

Abstract

We introduce a computationally efficient approach to calculating the characteristics of excitons in quantum wells. In this approach we derive a system of self-consistent equations describing the motion of an electron-hole pair. The motion in the growth direction of the quantum well in this approach is separated from the in-plane motion, but each of them occurs in modified potentials found self-consistently. The approach is applied to shallow quantum wells, for which we obtained an analytical expression for the exciton binding energy and the ground state eigenfunction. Our results are in excellent agreement with standard variational calculations, but require greatly reduced computational effort.