Trion clustering structure and binding energy in 2D semiconductor materials: Faddeev equations approach

TL;DR

This paper develops a formalism using Faddeev equations to study trions in 2D semiconductor materials, providing numerical solutions for binding energies and analyzing their structure with different interaction potentials.

Contribution

It introduces two regularization methods for solving Faddeev equations with repulsive potentials and applies them to calculate trion energies in MoS₂.

Findings

Trion binding energy in MoS₂ is approximately -49.5 meV.

The structure shows a strongly bound exciton weakly coupled to an electron.

Two regularization methods yield consistent energy results.

Abstract

In this work, we develop the basic formalism to study trions in semiconductor layered materials using the Faddeev equations in momentum space for three different particles lying in two dimensions. We solve the trion Faddeev coupled integral equations for both short-range one-term separable Yamaguchi potential and Rytova-Keldysh (RK) interaction applied to the MoS$_2$ layer. We devise two distinct regularization methods to overcome the challenge posed by the repulsive electron-electron RK potential in the numerical solution of the Faddeev equations in momentum space. The first method regulates the repulsive interaction in the infrared region, while the second regulates it in the ultraviolet region. By extrapolating the trion energy to the situation without screening, the two methods gave consistent results for the MoS$_2$ layer with a trion binding energy of $-49.5(1)$~meV for the exciton energy of $-753.3$~meV. We analyzed the trion structure for the RK and Yamaguchi potentials in detail, showing their overall similarities and the dominant cluster structure, where the strongly bound exciton is weakly bound to an electron. We found that this property is manifested in the dominance of two of the Faddeev components over the one where the hole is a spectator of the interacting electron pair.