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.

22 pages, 4 figures

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• Fast diffusion of water nanodroplets on graphene
• Anomalous Dynamical Behavior of Freestanding Graphene Membranes
• Unexpected catalytic activity of nanorippled graphene
• Graphene Ripples as a Realization of a Two-Dimensional Ising Model: A Scanning Tunneling Microscope Study
• Thermalized buckling of isotropically compressed thin sheets
• Effects of thermal rippling on the frictional properties of free-standing graphene
• Oscillations of van Hove singularities spacing induced by sub-Angstrom fluctuations of interlayer spacing in graphene superlattices
• Three-dimensional surface topography of graphene by divergent beam electron diffraction
• STM driven transition from rippled to buckled graphene in a spin-membrane model
• Defects induce phase transition from dynamic to static rippling in graphene
• Enhanced hydrogen-gas permeation through rippled graphene
• 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
• Apparent rippling with honeycomb symmetry and tunable periodicity observed by scanning tunneling microscopy on suspended graphene
• Permeation of hydrogen across graphdiyne: molecular dynamics vs. quantum simulations and role of membrane motion