Ratchet effect and amplitude dependence of phase locking in a two-dimensional Frenkel-Kontorova model

Abstract

We demonstrate the ratchet and phase locking effects in a two-dimensional overdamped Frenkel-Kontorova model with a square symmetric periodic substrate when both a longitudinal dc drive and a circular ac drive are applied. Besides the harmonic steps, the large half integer steps can also clearly be seen in the longitudinal (x) direction. These half integer steps are directly correlated to the appearance of positive and negative ratchet effects in the transverse (y) direction due to the symmetry breaking in the combination of the dc and ac drives. The angle between the net displacement and the longitudinal direction is analytically obtained in a single period of the ac drive. In the examination of the amplitude dependence of the ac drive, the maxima decrease monotonically with the amplitude, while the anomalies occur for the critical depinning force and the harmonic steps due to the spatial symmetry breaking of orbits in the presence of the ac drive.

Dynamic mode locking in a driven colloidal system: experiments and theory

“…Model systems composed of colloidal particles in periodic potentials have been studied for a number of years [28,29], from simple double well potentials [30][31][32][33] to directed motion [34][35][36][37][38][39], particle sorting [40], and kink generation [41] in two-dimensional (2D) optical lattices. Colloidal systems are easy to manipulate, and have accessible length and time scales, making them attractive models for the study of synchronisation at the microscale.…”

Rectification and phase locking of graphite

“…This study differs from the previous works [21,25]. The rectification of materials with triangular symmetry was studied in Ref.…”

“…[21], whereas that of the simple cubic symmetric materials was studied in Ref. [25]. The present study,unlike all other previous works, considers graphite.…”

“…Rectification of the simple cubic lattice and triangular lattice have been studied previously [21,25]. The present study considers graphene, which is much more interesting.…”

“…To understand these very complex physical systems, the focus was always on simple many-body models. Among them, the dissipative (overdamped) FrenkelKontorova (FK) model [21][22][23][24][25][26][27][28][29][30] is one of the simplest and most tractable, yet it is still able to describe the essence of many physical and biological phenomena.…”