Shapiro Steps Observed in a Two-Dimensional Yukawa Solid Modulated by a One-Dimensional Vibrational Periodic Substrate

TL;DR

This study uses simulations to observe Shapiro steps in a 2D dusty plasma modulated by a 1D vibrational substrate, revealing mode locking phenomena at specific frequency ratios.

Contribution

It is the first to identify and analyze multiple Shapiro steps in a 2D dusty plasma under a vibrational periodic substrate using Langevin dynamics.

Findings

Four significant Shapiro steps observed with increasing driving force.

Mode locking occurs when frequency ratios are near integers.

Transitions at the first and fourth steps are continuous, while others are discontinuous.

Abstract

Depinning dynamics of a two-dimensional (2D) solid dusty plasma modulated by a one-dimensional (1D) vibrational periodic substrate are investigated using Langevin dynamical simulations. As the uniform driving force increases gradually, from the overall drift velocity varying with the driving force, four significant Shapiro steps are discovered. The data analysis indicate that, when the ratio of the frequency from the drift motion over potential wells to the external frequency from the modulation substrate is close to integers, dynamic mode locking occurs, corresponding to the discovered Shapiro steps. Around both termini of the first and fourth Shapiro steps, the transitions are found to be always continuous, however, the transition between the second and third Shapiro steps is discontinuous, probably due to the different arrangements of particles.