A numerical study of the rippling instability driven by electron-phonon coupling in graphene

TL;DR

This study uses numerical methods to analyze how electron-phonon interactions induce rippling in finite graphene membranes, confirming a phase transition from flat to rippled states.

Contribution

It provides a detailed numerical analysis of rippling instability in finite graphene due to electron-phonon coupling, extending previous theoretical models.

Findings

Electron-phonon coupling induces a transition from flat to rippled phase.

Finite size effects are crucial in the rippling transition.

The model confirms the stability of rippled configurations at certain coupling strengths.

Abstract

Suspended graphene exhibits ripples of size ranging from 50 to 100 {\AA} and height $\sim$10{\AA}, however, their origin remains undetermined. Previous theoretical works have proposed that rippling in graphene might be generated by the coupling between the bending modes and the density of electrons. These studies theoretically proposed that in the thermodynamic limit a membrane of single layer graphene displays a lattice instability for large enough electron-phonon coupling, undergoing a phase transition from a flat phase to a rippled one. In this work we solve the elasticity equations for a finite membrane of graphene coupled to the charge distribution, modeled in the tight-binding approximation, we find that the electron-phonon coupling controls a transition from a stable flat configuration to a stable rippled phase.