On the locked dynamical states of an overdamped Josephson junction array

Abstract

We study the dynamics of a 2D array of Josephson junctions biased with both dc and ac currents. Within certain ranges of the dc current intensity a locking between the natural oscillation frequency of the array and that of the ac forcing term occurs, giving rise to periodic solutions. As expected, a set of Shapiro steps appears in the V -I curve. We show that there is no one-to-one correspondence between the value of V on the Shapiro step and the dynamical state of the array. In particular for a frustration equal to 0.5, besides the well-known ground state, g.s., of the array (the checkerboard-like vortex configuration), there exist other dynamical states accessible to the system. These latter are characterized by the same average voltage of the g.s. but different average energies and vortex configurations, with one or more domain walls. These 'new' states are stable against small thermal fluctuations and phase perturbations. A better insight into the physical conditions needed to generate them has been obtained by studying the dynamical behaviour of a ladder as a function of its size and of its orientation with respect to the external bias current The relevance of our observations to the experimental studies of the array dynamics performed on a microscopical scale is briefly discussed.

Transverse phase locking in fully frustrated Josephson junction arrays: A different type of fractional giant steps

“…x , must experience a similar abrupt transition of π, as can be seen from equation (11). We therefore claim that the apparent discrepancy observed between the numerical simulations and the perturbation theory near the roots of J 0…”

“…Inserting this solution (A 1 , B 1 ) for Ψ y into the Ψ y -linearized equation (11) gives the static properties:…”

“…In general, for f = p/q, the ground state has qa × qa superlattice structure, therefore the voltage for vortices moving with velocity u is 2πu/qa = v x , and phase-locking for the n-th harmonic is obtained at voltages V n,q = (n/q)Ω. This is the condition for the so-called "fractional giant Shapiro steps" 5,6,7,8,9,10,11 .…”

“…4 Fractional giant Shapiro steps at voltages V n,q = N n Ω/2eq, were observed experimentally 5,6 for strongly commensurate magnetic fields, f = p/q, with p, q integers, and extensively investigated in numerical simulations. 7,8,9,10,11 Also, subharmonic giant Shapiro steps at voltages V n,m = N n Ω/2em were observed experimentally 6 for zero magnetic field (f = 0), and attributed to the nucleation of complex collective dynamical states 12,13 induced by disorder or inductance effects. Shapiro-like phase-locking is also observed in the case of driven vortex lattices in bulk superconductors with two-dimensional periodic pinning arrays, as recently reported both experimentally 14 and theoretically.…”

“…The presence of a magnetic field (f = 0) breaks the axial symmetry in the direction of the bias current, and 2D-cooperative behavior may come into play. This leads to the well-known fractional giant Shapiro steps 5,6,7,8,9,10,11 induced by a longitudinal ac current. It also, as we will demonstrate in this paper, allows for transverse phase locking when the ac current is perpendicular to the dc current, since the two directions of motion become coupled.…”