The speed-locking effect of particles on a graphene layer with travelling surface wave

Fast diffusion induced by thermal fluctuation and vibration has been detected at nanoscales. In this paper, the movement of particle on a graphene layer with travelling surface wave is studied by molecular dynamics simulation and theoretical model. It is proved that the particle will keep moving at the wave speed with certain prerequisite conditions, namely speed-locking effect. By expressing van der Waals (vdW) potential between particle and wavy surface as a function of curvatures, the mechanism is clarified based on the puddle of potential in a relative wave-frame coordinate. Two prerequisite conditions are proposed: the initial position of particle should locate in the potential puddle, and the initial kinetic energy cannot drive particle to jump out of the potential puddle. The parametric analysis indicates that the speed-locking region will be affected by wavelength, amplitude and pair potential between particle and wave. With smaller wavelength, larger amplitude and stronger vdW potential, the speed-locking region is larger. This work reveals a new kind of coherent movement for particles on layered material based on the puddle potential theory, which can be an explanation for fast diffusion phenomena at nano scales.