Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives

TL;DR

This paper studies the complex nonlinear dynamics of particles on a symmetric 2D periodic substrate under combined dc and circular ac drives, revealing velocity steps, rectification effects, and phase diagrams influenced by disorder.

Contribution

It introduces a detailed analysis of particle motion under combined drives, identifying velocity quantization, rectification phenomena, and phase diagrams, supported by a simple model and disorder effects.

Findings

Discrete velocity steps occur at integer multiples of lattice constants and frequency.

Transverse rectification occurs without transverse dc drive, forming phase diagram tongues.

Disorder smears rectification regions and alters velocity steps.

Abstract

We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough ac drives, the particle orbit encircles one or more potential maxima of the periodic substrate. In this case, when an additional increasing dc drive is applied in the longitudinal direction, the longitudinal velocity increases in a series of discrete steps that are integer multiples of the lattice constant of the substrate times the frequency. Fractional steps can also occur. These integer and fractional steps correspond to distinct stable dynamical orbits. A number of these phases also show a rectification in the positive or negative transverse direction where a non-zero transverse velocity occurs in the absence of a dc transverse drive. We map out the phase diagrams of the regions of rectification as a function of ac amplitude, and find a series of tongues. Most of the features, including the steps in the longitudinal velocity and the transverse rectification, can be captured with a simple toy model and by arguments from nonlinear maps. We have also investigated the effects of thermal disorder and incommensuration on the rectification phenomena, and find that for increasing disorder, the rectification regions are gradually smeared and the longitudinal velocity steps are no longer flat but show a linearly increasing velocity.