# Many-body theory of optical absorption in doped two-dimensional semiconductors

## TL;DR

This paper develops a many-body theoretical framework to analyze optical absorption in doped two-dimensional semiconductors, revealing how doping influences exciton and trion spectral features through complex many-body interactions.

## Contribution

It introduces two approximate many-body models to study doping effects on optical spectra, including a scattering Hamiltonian and a Mahan-Nozieres-De Dominicis model, providing insights into Fermi-edge singularities.

## Key findings

- Spectra exhibit doping-dependent shifts and line shape changes.
- Identification of trion states as bound electron-exciton scattering states.
- Observation of Fermi-edge singularity signatures at high doping levels.

## Abstract

In this article, we use a many-body approach to study the absorption spectra of electron-doped two-dimensional semiconductors. Optical absorption is modeled by a many-body scattering Hamiltonian which describes an exciton immersed in a Fermi sea. The interaction between electron and exciton is approximated by an effective scattering potential, and optical spectra are calculated by solving for the exciton Green's function. From this approach, a trion state can be assigned as a bound state of an electron-exciton scattering process, and the doping-dependent phenomena observed in the spectra can be attributed to several many-body effects induced by the interaction with the Fermi sea. While the many-body scattering Hamiltonian can not solved exactly, we reduce the problem to two limiting solvable situations. The first approach approximates the full many-body problem by a simple scattering process between the electron and the exciton, with a self-energy obtained by solving a Bethe-Salpeter equation (BSE). An alternate approach assumes an infinite mass for the exciton, such that the many-body scattering Hamiltonian reduces to a Mahan-Nozieres-De Dominicis (MND) model. The exciton Green's function can then be solved numerically exactly by a determinantal formulation, and the optical spectra show signatures of the Fermi-edge singularity at high doping densities. The full doping dependence and temperature dependence of the exciton and trion lineshapes are simulated via these two approximate approaches, with the results compared to each other and to experimental expectations.