Kavli Affiliate: Mark J. Bowick
| First 5 Authors: Paul Z. Hanakata, Sourav S. Bhabesh, David Yllanes, David R. Nelson, Mark J. Bowick
| Summary:
Crystalline sheets (e.g., graphene and transition metal dichalcogenides)
liberated from a substrate are a paradigm for materials at criticality because
flexural phonons can fluctuate into the third dimension. Although studies of
static critical behaviors (e.g., the scale-dependent elastic constants) are
plentiful, investigations of dynamics remain limited. Here, we use molecular
dynamics to study the time dependence of the midpoint (the height
center-of-mass) of doubly clamped nanoribbons, as prototypical graphene
resonators, under a wide range of temperature and strain conditions. By
treating the ribbon midpoint as a Brownian particle confined to a nonlinear
potential (which assumes a double-well shape beyond the buckling transition),
we formulate an effective theory describing the ribbon’s tunneling rate across
the two wells and its oscillations inside a given well. We find that, for
nanoribbbons compressed above the Euler buckling point and thermalized above a
temperature at which the non-linear effects due to thermal fluctuations become
significant, the exponential term (the ratio between energy barrier and
temperature) depends only on the geometry, but not the temperature, unlike the
usual Arrhenius behavior. Moreover, we find that the natural oscillation time
for small strain shows a non-trivial scaling $tau_{rm o}sim
L_0^{,z}T^{-eta/4}$, with $L_0$ being the ribbon length, $z=2-eta/2$ being
the dynamic critical exponent, $eta=0.8$ being the scaling exponent describing
scale-dependent elastic constants, and $T$ being the temperature. These unusual
scale- and temperature-dependent dynamics thus exhibit dynamic criticality and
could be exploited in the development of graphene-based nanoactuators.
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