Analysis of rippling in incommensurate one-dimensional coupled chains

TL;DR

This paper introduces a new double chain model to analyze rippling phenomena in incommensurate one-dimensional coupled chains, providing insights into the relaxation mechanisms of layered 2D materials.

Contribution

It presents a novel application of the Frenkel-Kontorova model to study ripples in incommensurate coupled chains, focusing on ground state configurations and numerical simulations.

Findings

Identification of ripple patterns in ground states

Numerical simulation results of ripple formation

Insights into relaxation mechanisms of layered materials

Abstract

Graphene and other recently developed 2D materials exhibit exceptionally strong in-plane stiffness. Relaxation of few-layer structures, either free-standing or on slightly mismatched substrates occurs mostly through out-of-plane bending and the creation of large-scale ripples. In this work, we present a novel double chain model, where we allow relaxation to occur by bending of the incommensurate coupled system of chains. As we will see, this model can be seen as a new application of the well-known Frenkel-Kontorova model for a one-dimensional atomic chain lying in a periodic potential. We focus in particular on modeling and analyzing ripples occurring in ground state configurations, as well as their numerical simulation.