Rectification and phase locking for particles on symmetric two-dimensional periodic substrates

We demonstrate a rectification phenomenon for overdamped particles interacting with a 2D symmetric periodic substrate when driven with a dc and a circular ac drive. As a function of longitudinal dc amplitude, the longitudinal velocity increases in a series of quantized steps distinct from Shapiro steps with transverse rectification occurring near these transitions. The rectification phenomenon is explained using symmetry arguments and a simple model.