Phase Locking, Devil's Staircases, Farey Trees, and Arnold Tongues in Driven Vortex Lattices with Periodic Pinning

TL;DR

This paper uses numerical simulations to explore complex dynamical phenomena such as phase locking, Devil's staircases, and Arnold tongues in vortex lattices driven over periodic pinning arrays, revealing rich structures in transport measurements.

Contribution

It demonstrates the presence of intricate dynamical structures like Devil's staircases and Arnold tongues in driven vortex lattices, linking these phenomena to specific vortex flow patterns and pinning array symmetries.

Findings

Devil's staircase structure observed in transverse voltage curves.

Plateaus correspond to distinct dynamical vortex phases.

Rich phase locking phenomena occur near symmetry directions.

Abstract

Using numerical simulations, we observe phase locking, Arnold tongues, and Devil's staircases for vortex lattices driven at varying angles with respect to an underlying superconducting periodic pinning array. This rich structure should be observalble in transport measurments. The transverse $V(I)$ curves have a Devil's staircase structure, with plateaus occurring near the driving angles along symmetry directions of the pinning array. Each of the plateaus corresponds to a different dyanmical phase with a distinctive vortex structure and flow pattern.