Scaling Properties of Flexible Membranes from Atomistic Simulations: Application to Graphene

TL;DR

This study investigates the scaling behavior of crystalline membranes, specifically graphene, using atomistic simulations to confirm the continuum membrane theory's predictions at microscopic scales.

Contribution

It introduces a Monte Carlo sampling method with collective atomic moves to analyze long-wavelength membrane behavior in graphene.

Findings

G(q) follows a power-law with exponent ~0.85 for both models

Supports the validity of membrane scaling theory for graphene

Demonstrates the effectiveness of wave move sampling in finite systems

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 quasi-harmonic model potential and for a realistic potential for graphene. To access the long wavelength limit for finite-size systems (up to 40000 atoms) we introduce a Monte Carlo sampling based on collective atomic moves (wave moves). We find a power-law behaviour $G(q)\propto q^{-2+\eta}$ with the same exponent $\eta \approx 0.85$ 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 like graphene.