Scaling properties of flexible membranes from atomistic simulations: Application to graphene

Abstract

Structure and thermodynamics of crystalline membranes are characterized by the long-wavelength behavior of the normal-normal correlation function $G(q)$. We calculate $G(q)$ by Monte Carlo and molecular dynamics simulations for a quasiharmonic model potential and for a realistic potential for graphene. To access the long-wavelength limit for finite-size systems (up to $40\text{ }000\text{ }\text{atoms}$) we introduce a Monte Carlo sampling based on collective atomic moves (wave moves). We find a power-law behavior $G(q)\ensuremath{\propto}{q}^{\ensuremath{-}2+\ensuremath{\eta}}$ with the same exponent $\ensuremath{\eta}\ensuremath{\approx}0.85$ for both potentials. This finding supports, from the microscopic side, the adequacy of the scaling theory of membranes in the continuum medium approach, even for an extremely rigid material such as graphene.