Phononic Casimir corrections for Graphene resonator

By calculating a Casimir energy for the acoustic phonons of Graphene, we find some temperature-dependent corrections for the pretension of a Graphene sheet suspended on a trench. We obtain values of the order of few mN/m for these corrections in fully as well as doubly clamped Graphene on a narrow trench with one nanometer width, at room temperature. These values are considerable compared to the experimental values, and can increase the fundamental resonance frequency of the Graphene. The values of these corrections increase by increasing the temperature, and so they can be utilized for tuning the Graphene pretension.