Critical radius and temperature for buckling in graphene

TL;DR

This paper analytically investigates the buckling behavior of suspended circular graphene membranes, identifying critical conditions for buckling modes influenced by electron-phonon coupling, with implications for experimental verification and material property estimation.

Contribution

It provides an analytical solution for buckling in graphene considering electron-phonon interactions and identifies critical parameters for buckling onset.

Findings

Buckling occurs at high critical temperatures or small radii.

Different buckling modes bifurcate from the flat membrane.

Results suggest feasible experiments to verify buckling behavior.

Abstract

In this work, we find an analytical flat-membrane solution to the saddle point equations, derived by Guinea et al. [Phys. Rev. B 89, 125428 (2014)], for the case of a suspended graphene membrane of circular shape. We also find how different buckled membrane solutions bifurcate from the flat membrane at critical temperatures and membrane radii. The saddle point equations take into account electron-phonon coupling and this coupling provides a residual stress even for a flat graphene layer. Below a critical temperature (which is exceedingly high for an infinite layer) or above a critical size that depend on boundary conditions, different buckling modes that may be the germ of rippling appear. Our results provide the opportunity to develop new feasible experiments dealing with buckling in small suspended graphene membranes that could verify them. These experiments may also be used to fit the phonon-electron coupling constant or the bending energy.