Flexural phonons in supported graphene: from pinning to localization

TL;DR

This paper explores the potential for Anderson localization of flexural phonons in supported graphene, revealing unique scattering properties and implications for thermal conductance, with a focus on disorder-induced pinning effects.

Contribution

It demonstrates the possibility of observing Anderson localization of flexural phonons in supported graphene and analyzes their statistical properties in the presence of substrate pinning centers.

Findings

Flexural phonons can exhibit Anderson localization in supported graphene.

Scattering time for flexural phonons remains finite as wave vector approaches zero.

Localized flexural phonons may influence electronic thermal conductance.

Abstract

We identify graphene layer on a disordered substrate as a possible system where Anderson localization of phonons can be observed. Generally, observation of localization for scattering waves is not simple, because the Rayleigh scattering is inversely proportional to a high power of wavelength. The situation is radically different for the out of plane vibrations, so-called flexural phonons, scattered by pinning centers induced by a substrate. In this case, the scattering time for vanishing wave vector tends to a finite limit. One may, therefore, expect that physics of the flexural phonons exhibits features characteristic for electron localization in two dimensions, albeit without complications caused by the electron-electron interactions. We confirm this idea by calculating statistical properties of the Anderson localization of flexural phonons for a model of elastic sheet in the presence of the pinning centers. Finally, we discuss possible manifestations of the flexural phonons, including the localized ones, in the electronic thermal conductance.