Collective excitations of graphene excitons being in the Bose-Einstein condensate state

TL;DR

This paper models the collective excitations of Bose-Einstein condensed excitons in graphene, deriving quantum hydrodynamic equations and revealing that their excitation frequency scales with the square root of the wave vector.

Contribution

It introduces a spinor equation for graphene excitons and derives quantum hydrodynamic equations to describe their collective excitations in the BEC state.

Findings

Collective excitation frequency scales as √k.

Quantum hydrodynamic equations for graphene excitons are established.

Bose-Einstein condensation of excitons in graphene is analyzed.

Abstract

Bose-Einstein condensation of the excitons in graphene is considered. We suggested the model spinor equation for neutral particles with short range interaction described the microscopic graphene excitons dynamic. Using this equation we derived quantum hydrodynamic equations for description of collective properties of excitons in graphene, particularly for the case when excitons being in the Bose-Einstein condensate (BEC) state. The dispersion of collective excitations in graphene excitons BEC is studied. We shown that frequency of collective excitations is proportional to the square root of the wave vector module: $\omega\sim \sqrt{k}$.