FROM PINNING TO LOCALIZATION IN GRAPHENE – ON THE STATISTICAL PROPERTIES OF RANDOMLY PINNED FLEXURAL PHONONS
Abstract
We identify graphene layer on a disordered substrate as a 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, and contribution to the electron dephasing rate.
Subject
flexrual phononGaussian orthogonal ensemble
nonlinear sigma model
random matrix theory
Graphene
inverse participation ratio
finite difference method
anomalously localized state
weak localization
Anderson localization
Citation
Zhao, Wei (2017). FROM PINNING TO LOCALIZATION IN GRAPHENE – ON THE STATISTICAL PROPERTIES OF RANDOMLY PINNED FLEXURAL PHONONS. Doctoral dissertation, Texas A & M University. Available electronically from https : / /hdl .handle .net /1969 .1 /173225.