Coupling of two Dirac particles

TL;DR

This paper investigates exciton formation from two Dirac particles in gapped graphene, deriving analytical solutions for wave functions and energy dispersions, highlighting how energy gaps and layer separation influence exciton properties.

Contribution

It provides analytical solutions for exciton wave functions and energy dispersions in gapped graphene systems, considering Coulomb interactions and interlayer separation.

Findings

Energy spectrum depends on energy gaps and layer separation.

Effective exciton mass varies with energy gaps and interlayer distance.

Analytical wave functions are derived for two Dirac particles with Coulomb interaction.

Abstract

A study of the formation of excitons as a problem of two Dirac particles in a gapped graphene layer and in two gapped graphene layers separated by a dielectric is presented. In the low energy limit the separation of the center-of-mass and relative motions is obtained. Analytical solutions for the wave function and energy dispersion for both cases when electron and hole interact via a Coulomb potential are found. It is shown that the energy spectrum and the effective exciton mass are functions of the energy gaps as well as interlayer separation in case of two layer gapped graphene.