Nonlinear Driven Response of a Phase-Field Crystal in a Periodic Pinning Potential

TL;DR

This paper investigates the nonlinear driven response and depinning transitions of a phase-field crystal model in periodic pinning potentials, revealing continuous and discontinuous transitions with hysteresis in one and two dimensions.

Contribution

It introduces a numerical study of the phase diagram and nonlinear response of a phase-field crystal model with periodic pinning, including novel findings on depinning transitions and hysteresis.

Findings

Depinning transitions are continuous at high pinning strength with power-law velocity-force relations.

Discontinuous depinning with hysteresis occurs at weak pinning potentials, even in one dimension.

Transverse depinning transitions are observed in two-dimensional systems.

Abstract

We study numerically the phase diagram and the response under a driving force of the phase field crystal model for pinned lattice systems introduced recently for both one and two dimensional systems. The model describes the lattice system as a continuous density field in the presence of a periodic pinning potential, allowing for both elastic and plastic deformations of the lattice. We first present results for phase diagrams of the model in the absence of a driving force. The nonlinear response to a driving force on an initially pinned commensurate phase is then studied via overdamped dynamic equations of motion for different values of mismatch and pinning strengths. For large pinning strength the driven depinning transitions are continuous, and the sliding velocity varies with the force from the threshold with power-law exponents in agreement with analytical predictions. Transverse depinning transitions in the moving state are also found in two dimensions. Surprisingly, for sufficiently weak pinning potential we find a discontinuous depinning transition with hysteresis even in one dimension under overdamped dynamics. We also characterize structural changes of the system in some detail close to the depinning transition.