Unusual ultralow frequency fluctuations in freestanding graphene

Abstract

Intrinsic ripples in freestanding graphene have been exceedingly difficult to study. Individual ripple geometry was recently imaged using scanning tunneling microscopy, but these measurements are limited to static configurations. Thermally-activated flexural phonon modes should generate dynamic changes in curvature. Here we show how to track the vertical movement of a one-square-angstrom region of freestanding graphene using scanning tunneling microscopy, thereby allowing measurement of the out-of-plane time trajectory and fluctuations over long time periods. We also present a model from elasticity theory to explain the very-low-frequency oscillations. Unexpectedly, we sometimes detect a sudden colossal jump, which we interpret as due to mirror buckling. This innovative technique provides a much needed atomic-scale probe for the time-dependent behavior of intrinsic ripples. The discovery of this novel progenitor represents a fundamental advance in the use of scanning tunneling microscopy, which together with the application of a thermal load provides a low-frequency nano-resonator.

arXiv comment22 pages, 4 figures

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• Unexpected catalytic activity of nanorippled graphene
• Rippling and crumpling in disordered free-standing graphene
• Fluctuation-induced current from freestanding graphene: toward nanoscale energy harvesting
• Graphene Ripples as a Realization of a Two-Dimensional Ising Model: A Scanning Tunneling Microscope Study
• The shallow shell approach to Pogorelov's problem and the breakdown of `mirror buckling'
• Effects of thermal rippling on the frictional properties of free-standing graphene
• Thermalized buckling of isotropically compressed thin sheets
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• Critical radius and temperature for buckling in graphene
• Three-dimensional surface topography of graphene by divergent beam electron diffraction
• Defects induce phase transition from dynamic to static rippling in graphene
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• Limits of stability in supported graphene nanoribbons subject to bending
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• Multifractal wave functions of charge carriers in graphene with folded deformations, ripples or uniaxial flexural modes: analogies to the quantum Hall effect under random pseudomagnetic fields
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• Permeation of hydrogen across graphdiyne: molecular dynamics vs. quantum simulations and role of membrane motion