Trions in coupled quantum wells and Wigner crystallization

TL;DR

This paper analytically investigates the properties of indirect trions in coupled quantum wells, predicts their Wigner crystallization at low densities, and compares their critical density to that of electron Wigner crystals.

Contribution

It provides analytical solutions for the energy spectrum and wave functions of indirect trions in coupled quantum wells and predicts Wigner crystallization of these trions.

Findings

Analytical energy spectrum and wave functions for indirect trions.

Prediction of 2D Wigner crystal formation of trions.

Critical density for trion Wigner crystal exceeds that of electron Wigner crystal.

Abstract

We consider a restricted three body problem, where two interacted particles are located in two dimensional (2D) plane and interact with the third one located in the parallel spatially separated plane. The system of such type can be formed in the semiconductor coupled quantum wells, where the electrons (or holes) and direct excitons spatially separated in different parallel neighboring quantum wells that are sufficiently close to interact and form negative X- or positive X+ indirect trions. It is shown that at large interwell separations, when the interwell separation much greater than the exciton Bohr radius, this problem can be solved analytically using the cluster approach. Analytical results for the energy spectrum and the wave functions of the spatially indirect trion are obtained, their dependence on the interwell separations is analyzed and a conditional probability distribution is calculated. The formation of 2D Wigner crystal of trions at the low densities is predicted. It is shown that the critical density of the formation of the trion Wigner crystal is sufficiently greater than the critical density of the electron Wigner crystal.