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

Abstract

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 $10^{-7}$ Å${}^{-1}$ till 10 Å${}^{-1}$ 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 $10^{-2}$ Å${}^{-1}$ till 1 Å${}^{-1}$. In the limit $q\to 0$ our data for the exponent $\eta$ of the renormalized bending rigidity ${\kappa }_R(q)\propto q^{-\eta }$ is compatible with the previously known analytical results for the SCSA $\eta \simeq 0.82$. However, this limit appears to be reached only for $q<10^{-5}$ Å${}^{-1}$ whereas at intermediate $q$ the behavior of $G(q)$ cannot be described by a single exponent.

5 pages, 4 figures

References in corpus (9)

• Electric Field Effect in Atomically Thin Carbon Films
• The structure of suspended graphene sheets
• Macroscopic graphene membranes and their extraordinary stiffness
• Electron scattering on microscopic corrugations in graphene
• Finite temperature lattice properties of graphene beyond the quasiharmonic approximation
• Graphene as an electronic membrane
• Gauge field induced by ripples in graphene
• Crumpling transition and flat phase of polymerized phantom membranes
• Thermal fluctuations of free standing graphene

Cited by in corpus (6)

• Limits on electron quality in suspended graphene due to flexural phonons
• Suppression of anharmonicities in crystalline membranes by external strain
• Temperature dependent resistivity in bilayer graphene due to flexural phonons
• Electron-induced rippling in graphene
• Nonlocal effective average action approach to crystalline phantom membranes
• Flexuron, a self-trapped state of electron in crystalline membranes