Lattice mismatch induced ripples and wrinkles in planar graphene/boron nitride superlattices

TL;DR

This paper develops a continuum model to explain how lattice mismatch causes ripple formation in graphene/boron nitride superlattices, predicting optimal ripple wavelengths that match atomic-scale calculations.

Contribution

It introduces a continuum theoretical framework for ripple formation in superlattices due to lattice mismatch, linking energy competition to ripple wavelength prediction.

Findings

Optimal ripple wavelengths depend on superlattice pitch.

Continuum theory predictions agree with atomic-scale calculations.

Lattice mismatch induces instability leading to ripple formation.

Abstract

A continuum theory to describe periodic ripple formation in planar graphene/boron nitride superlattices is formulated. Due to the lattice mismatch between the two materials, it is shown that flat superlattices are unstable with respect to ripple formation of appropriate wavelengths. A competition between bending energy and transverse stretching energy gives rise to an optimal ripple wavelength that depends on the superlattice pitch. The optimal wavelengths predicted by the continuum theory are in good agreement with atomic scale total energy calculations previously reported in Nandwana and Ertekin, Nano Lett. 15 1468 (2015).