Journal
SCIENTIFIC REPORTS
Volume 8, Issue -, Pages -Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/s41598-018-34426-3
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Funding
- Russian Science Foundation [14-42-00044]
- U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering [DE-SC0014154]
- U.S. Department of Energy (DOE) [DE-SC0014154] Funding Source: U.S. Department of Energy (DOE)
- Russian Science Foundation [17-42-00003] Funding Source: Russian Science Foundation
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We identify graphene layer on a disordered substrate as a system where 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.
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