Transverse phase-locking in fully frustrated Josephson junction arrays: a new type of fractional giant steps

TL;DR

This paper investigates transverse phase-locking phenomena in fully frustrated Josephson junction arrays, revealing unique current-voltage steps, hysteresis, and dynamical instabilities, with a theoretical model explaining the observed behaviors.

Contribution

It introduces a novel analysis of transverse ac-drive effects on vortex lattice phase locking, differing from traditional Shapiro steps, and provides a simplified four-plaquette model for large arrays.

Findings

Phase locking shows unique dependence on transverse ac amplitude.

Critical current increases with transverse ac-drive, decreases with longitudinal.

Dynamical instabilities and hysteresis occur at larger ac amplitudes.

Abstract

We study, analytically and numerically, phase locking of driven vortex lattices in fully-frustrated Josephson junction arrays at zero temperature. We consider the case when an ac current is applied {\it perpendicular} to a dc current. We observe phase locking, steps in the current-voltage characteristics, with a dependence on external ac-drive amplitude and frequency qualitatively different from the Shapiro steps, observed when the ac and dc currents are applied in parallel. Further, the critical current increases with increasing transverse ac-drive amplitude, while it decreases for longitudinal ac-drive. The critical current and the phase-locked current step width, increase quadratically with (small) amplitudes of the ac-drive. For larger amplitudes of the transverse ac-signal, we find windows where the critical current is hysteretic, and windows where phase locking is suppressed due to dynamical instabilities. We characterize the dynamical states around the phase-locking interference condition in the $IV$ curve with voltage noise, Lyapunov exponents and Poincar\'e sections. We find that zero temperature phase-locking behavior in large fully frustrated arrays is well described by an effective four plaquette model.