The ac-Driven Motion of Dislocations in a Weakly Damped Frenkel-Kontorova Lattice

TL;DR

This paper demonstrates through numerical simulations that ac fields can support stable moving dislocations in a weakly damped Frenkel-Kontorova lattice, revealing two dislocation types and threshold conditions for their motion.

Contribution

It introduces a method to generate and sustain moving dislocations in a uniform FK lattice using ac driving near the gap frequency, expanding understanding of nonlinear excitations.

Findings

Stable moving dislocations can be supported by ac driving.

Two types of dislocations observed: broad and localized.

Threshold amplitude depends on friction and does not vanish at zero friction.

Abstract

By means of numerical simulations, we demonstrate that ac field can support stably moving collective nonlinear excitations in the form of dislocations (topological solitons, or kinks) in the Frenkel-Kontorova (FK) lattice with weak friction, which was qualitatively predicted by Bonilla and Malomed [Phys. Rev. B{\bf 43}, 11539 (1991)]. Direct generation of the moving dislocations turns out to be virtually impossible; however, they can be generated initially in the lattice subject to an auxiliary spatial modulation of the on-site potential strength. Gradually relaxing the modulation, we are able to get the stable moving dislocations in the uniform FK lattice with the periodic boundary conditions, provided that the driving frequency is close to the gap frequency of the linear excitations in the uniform lattice. The excitations have a large and noninteger index of commensurability with the lattice (suggesting that its actual value is irrational). The simulations reveal two different types of the moving dislocations: broad ones, that extend, roughly, to half the full length of the periodic lattice (in that sense, they cannot be called solitons), and localized soliton-like dislocations, that can be found in an excited state, demonstrating strong persistent internal vibrations. The minimum (threshold) amplitude of the driving force necessary to support the traveling excitation is found as a function of the friction coefficient. Its extrapolation suggests that the threshold does not vanish at the zero friction, which may be explained by radiation losses. The moving dislocation can be observed experimentally in an array of coupled small Josephson junctions in the form of an {\it inverse Josephson effect}, i.e., a dc-voltage response to the uniformly applied ac bias current.