Subharmonic Shapiro steps in depinning dynamics of a 2D solid dusty plasma modulated by 1D nonlinear deformed periodic substrates

TL;DR

This study uses simulations to explore how a 2D dusty plasma interacts with nonlinear deformed substrates under combined forces, revealing subharmonic and harmonic Shapiro steps due to mode locking, influenced by substrate deformation.

Contribution

It demonstrates the impact of nonlinear deformed substrates on Shapiro steps in dusty plasma depinning dynamics, highlighting the role of substrate deformation and particle coordination in mode locking.

Findings

Subharmonic and harmonic Shapiro steps are observed under combined DC and AC forces.

Nonlinear deformed substrates significantly influence the formation of Shapiro steps.

Particle motion at subharmonic steps is less synchronized, indicating instability.

Abstract

Langevin dynamical simulations are performed to investigate the depinning dynamics of a two-dimensional solid dusty plasma, which is modulated by one-dimensional nonlinear deformed periodic substrates, and also driven by the combination of the DC and AC forces. As the DC driving force increases gradually, pronounced subharmonic and harmonic Shapiro steps are discovered under the combined modulation of the deformed substrate and the external AC drive. These observed subharmonic and harmonic Shapiro steps are attributed to the dynamic mode locking. The data analysis results indicate that the nonlinear deformed substrate strongly influences these subharmonic Shapiro steps, which can be accurately diagnosed using the fraction of sixfold coordinated particles. Furthermore, the diagnostic of the kinetic temperature clearly indicates the difference between harmonic and subharmonic Shapiro steps, i.e., the particle motion is slightly less synchronized at subharmonic Shapiro steps, caused by the unstable locations of the deformed substrate.