Ripples in a graphene membrane coupled to Glauber spins

TL;DR

This paper develops a theoretical model for ripples in suspended graphene, coupling elasticity with Glauber spin dynamics, revealing long-lived metastable ripple states independent of temperature.

Contribution

It introduces a novel coupling of graphene elasticity with Glauber spins to explain ripple formation and stability.

Findings

Ripples appear as metastable states with no preferred orientation.

Long-lived ripples occur at any temperature due to slow spin dynamics.

Numerical solutions support the theoretical model.

Abstract

We propose a theory of ripples in suspended graphene sheets based on two-dimensional elasticity equations that are made discrete on the honeycomb lattice and then periodized. At each point carbon atoms are coupled to Ising spins whose values indicate the atoms local trend to move vertically off-plane. The Ising spins are in contact with a thermal bath and evolve according to Glauber dynamics. In the limit of slow spin flip compared to membrane vibrations, ripples with no preferred orientation appear as long-lived metastable states for any temperature. Numerical solutions confirm this picture.