Effects of Spatial Dispersion on the Casimir Force between Graphene Sheets

TL;DR

This paper studies how spatial dispersion affects the Casimir force between graphene sheets, considering temperature effects, chemical potential, and energy gaps, revealing that dispersion influences the force mainly at finite temperatures and when graphene's conductivity is reduced.

Contribution

It provides a detailed analysis of spatial dispersion effects on the Casimir force in graphene, especially under conditions of finite temperature and induced band gaps, which was not thoroughly explored before.

Findings

Quantum interaction remains distance-dependent regardless of dispersion.

Finite temperature Casimir force is mainly affected by the zero Matsubara term.

Inducing a band gap makes graphene a poorer conductor, amplifying dispersion effects.

Abstract

The Casimir force between graphene sheets is investigated with emphasis on the effect from spatial dispersion using a combination of factors, such as a nonzero chemical potential and an induced energy gap. We distinguish between two regimes for the interaction - T=0 $K$ and $T\neq 0$ $K$. It is found that the quantum mechanical interaction (T=0 $K$) retains its distance dependence regardless of the inclusion of dispersion. The spatial dispersion from the finite temperature Casimir force is found to contribute for the most part from $n=0$ Matsubara term. These effects become important as graphene is tailored to become a poor conductor by inducing a band gap.