Casimir energy for acoustic phonons in graphene

Abstract

We find the Casimir energy, at finite temperature, for acoustic phonons in a graphene sheet suspended over a rectangular trench, and the corresponding Casimir forces are interpreted as correction terms to the built-in tensions of the graphene. We show that these corrections generally break the tensional isotropy of the membrane, and can increase or decrease the membrane tension. We demonstrate that for a narrow rectangular trench with side-lengths in the order of few nanometers and few micrometers, these temperature corrections are expected to be noticeable at room temperature. These corrections would be even more considerable by increasing the temperature, and can be applied for adjusting the built-in tension of the graphene. Consequently we introduce a corrected version for the fundamental resonance frequency of the graphene resonator.