Exact solution of an exciton energy for a monolayer medium

TL;DR

This paper derives exact solutions for exciton energy spectra in a monolayer medium by modeling excitons as relativistic fermions, providing analytical results that align with existing literature and predicting exciton decay times.

Contribution

It introduces an exact analytical approach to calculate exciton energies in a monolayer, modeling them as relativistic fermions with Coulomb interaction, which is novel.

Findings

Binding energies agree with literature

Derived exciton decay times

Analytical solutions for Coulomb potential

Abstract

We present exact solutions of an energy spectrum of 2-interacting particles in which they seem to be relativistic fermions in 2+1 space-time dimensions. The 2x2 spinor equations of 2-interacting fermions through general central potential were separated covariantly into the relative and center of mass coordinates. First of all, the coupled first order differential equations depending on radial coordinate were derived from 2x2 spinor equations. Then, a second order radial differential equation was obtained and solved for Coulomb interaction potential. We apply our solutions to exciton phenomena for a free-standing monolayer medium. Since we regard exciton as isolated 2-interacting fermions in our model, any other external effect such as substrate was eliminated. Our results show that the obtained binding energies in our model are in agreement with the literature. Moreover, the decay time of an exciton was found out spontaneously in our calculations.