Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene

Understand

Crystalline membranes at finite temperatures have an anomalous behavior of the bending rigidity that makes them more rigid in the long wavelength limit.

• This issue is particularly relevant for applications of graphene in nano- and micro-electromechanical systems.
• We calculate numerically the height-height correlation function $G(q)$ of crystalline two-dimensional membranes, determining the renormalized bending rigidity, in the range of wavevectors $q$ from $10^{-7}$ \AA$^{-1}$ till 10 \AA$^{-1}$ in the self-consistent screening approximation (SCSA).
• For parameters appropriate to graphene, the calculated correlation function agrees reasonably with the results of atomistic Monte Carlo simulations for this material within the range of $q$ from $10^{-2}$ \AA$^{-1}$ till 1 \AA$^{-1}$.