Many-body theory of radiative lifetimes of exciton-trion superposition states in doped two-dimensional materials

TL;DR

This paper develops a many-body theoretical framework to calculate radiative lifetimes of exciton-trion superposition states in doped 2D materials, revealing their dependence on momentum and doping density.

Contribution

It introduces a novel many-body formalism to analyze radiative lifetimes of exciton-trion superpositions in doped 2D materials, accounting for their complex coupling and momentum-dependent emission properties.

Findings

Lifetimes range from hundreds of femtoseconds to nanoseconds depending on momentum.

Lifetimes are strongly influenced by doping density.

Superposition states exhibit distinct radiative behaviors inside and outside the light cone.

Abstract

Optical absorption and emission spectra of doped two-dimensional (2D) materials exhibit sharp peaks that are often identified with pure excitons and pure trions (or charged excitons), but both peaks have been recently attributed to superpositions of 2-body exciton and 4-body trion states and correspond to the approximate energy eigenstates in doped 2D materials. In this paper, we present the radiative lifetimes of these exciton-trion superposition energy eigenstates using a many-body formalism that is appropriate given the many-body nature of the strongly coupled exciton and trion states in doped 2D materials. Whereas the exciton component of these superposition eigenstates are optically coupled to the material ground state, and can emit a photon and decay into the material ground state provided the momentum of the eigenstate is within the light cone, the trion component is optically coupled only to the excited states of the material and can emit a photon even when the momentum of the eigenstate is outside the light cone. In an electron-doped 2D material, when a 4-body trion state with momentum outside the light cone recombines radiatively, and a photon is emitted with a momentum inside the light cone, the excess momentum is taken by an electron-hole pair left behind in the conduction band. The radiative lifetimes of the exciton-trion superposition states, with momenta inside the light cone, are found to be in the few hundred femtoseconds to a few picoseconds range and are strong functions of the doping density. The radiative lifetimes of exciton-trion superposition states, with momenta outside the light cone, are in the few hundred picoseconds to a few nanoseconds range and are again strongly dependent on the doping density.