Exact solution of an exciton energy for a monolayer medium

Abstract

We present exact solutions of an energy spectrum of 2-interacting particles in which they seem to be relativistic fermions in 2\u2009+\u20091 space-time dimensions. The 2\u2009×\u20092 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 2\u2009×\u20092 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.