Phase Locking and Fractional Shapiro Steps in Collective Dynamics of Microparticles

In driven nonlinear systems, phase locking is an intriguing effect leading to robust stationary states that are stable over extended ranges of control parameters. Recent experiments allow for exploring microscopic mechanisms underlying such phenomena in collective dynamics of micro- and nanoparticles. Here, we show that phase-locked dynamics of hardcore-interacting microparticles in a densely populated periodic potential under time-periodic driving arises from running solitary cluster waves. We explain how values of phase-locked currents are related to soliton velocities and why collective particle dynamics synchronize with the driving for certain particle diameters only. Our analysis is based on an effective potential for the solitary wave propagation and a unit displacement law, which states that the total average shift of all particle positions per soliton period equals one wavelength of the periodic potential.