Stability of suspended graphene under Casimir force

We consider a graphene sheet suspended above a conducting surface. Treating graphene as an elastic membrane subjected to Casimir force, we study its stability against sagging towards the conductor. There exists a critical elevation at the edges below which the central part of the suspended graphene nucleates a trunk that sinks under the action of the Casimir force. The dependence of the critical elevation on temperature, dimensions, and the elastic stress applied to the graphene sheet is computed.

Figure 1

Suspended graphene attracted to a solid surface by Casimir force.

Figure 2

Casimir-driven sagging and instability of a rectangular graphene sheet against attachment to the underlying surface.

Figure 3

Profile of a sagging graphene due to Casimir force for three values of parameter $l={\gamma }^{1/2}L/a$. At $l=0.1$ the effect of Casimir attraction is weak, while at $l=0.44$ the graphene sheet is close to the critical separation below which it becomes unstable against sagging all the way down to the conductor.