Thermal fluctuations of free standing graphene

TL;DR

This paper employs non-perturbative renormalization group methods to analyze thermal fluctuations in free-standing graphene, revealing a crossover from perturbative to anomalous behavior and supporting its description as a tethered membrane.

Contribution

It introduces a self-consistent RG approach to compute momentum-dependent elastic constants, providing new insights into graphene's fluctuation behavior and ripples.

Findings

Identifies a sharp crossover scale in thermal fluctuations.

Matches Monte Carlo results for graphene.

Supports the tethered membrane model for graphene.

Abstract

We use non-perturbative renormalization group techniques to calculate the momentum dependence of thermal fluctuations of graphene, based on a self-consistent calculation of the momentum dependent elastic constants of a tethered membrane. We find a sharp crossover from the perturbative to the anomalous regime, in excellent agreement with Monte Carlo results for graphene, and give an accurate value for the crossover scale. Our work strongly supports the notion that graphene is well described as a tethered membrane. Ripples emerge naturally from our analysis.