Efficient calculation of trion energies in monolayer transition metal dichalcogenides

TL;DR

This paper presents an efficient method for calculating trion energies in monolayer transition metal dichalcogenides by solving the three-body Schrödinger equation in momentum space, improving accuracy over previous approaches.

Contribution

The authors introduce a novel computational approach using the Landé subtraction method to accurately compute trion binding energies directly from the three-body Schrödinger equation.

Findings

Results agree with quantum Monte Carlo calculations.

The method yields a larger trion-to-exciton binding energy ratio.

Approach can be extended to other 2D semiconductor few-body problems.

Abstract

The reduced dielectric screening in atomically thin semiconductors leads to remarkably strong electron interactions. As a result, bound electron-hole pairs (excitons) and charged excitons (trions), which have binding energies in the hundreds and tens of meV, respectively, typically dominate the optical properties of these materials. However, the long-range nature of the interactions between charges represents a significant challenge to the exact calculation of binding energies of complexes larger than the exciton. Here, we demonstrate that the trion binding energy can be efficiently calculated directly from the three-body Schr\"odinger equation in momentum space. Key to this result is a highly accurate way of treating the pole of the electronic interactions at small momentum exchange (i.e., large separation between charges) via the Land\'e subtraction method. Our results are in excellent agreement with quantum Monte Carlo calculations, while yielding a substantially larger ratio of the trion to exciton binding energies than obtained in recent variational calculations. Our numerical approach may be extended to a host of different few-body problems in 2D semiconductors, and even potentially to the description of exciton polarons.