Modelling Spontaneous Thermal Fluctuations of Ripples in Suspended Graphene

At room temperature, micron-size sheets of freestanding graphene are in constant motion, even in the presence of an applied
bias voltage. A key mechanism behind this result is the stochastic curvature inversion of ripples, during which thousands of atoms move
coherently with long-time correlations. We present a Langevin model that captures this out-of-plane motion unique to two-dimensional
materials. In particular, we model the membrane atoms closer to the scanning tunneling microscopy tip as a Brownian particle in a double-well potential, which represents the convex and concave curvature states of the ripple. In addition, we compute the average generated power using the stochastic thermodynamics formalism.