Row-switched states in two-dimensional underdamped Josephson-junction arrays

Abstract

When magnetic flux moves across layered or granular superconductor structures, the passage of vortices can take place along channels which develop finite voltage, while the rest of the material remains in the zerovoltage state. We study analytically an example of such mixed dynamics: the row-switched ͑RS͒ states in underdamped two-dimensional Josephson arrays, driven by a uniform dc current under external magnetic field but neglecting self-fields. The governing equations are cast into a compact differential-algebraic system which describes the dynamics of an assembly of Josephson oscillators coupled through the mesh current. We carry out a formal perturbation expansion, and obtain the dc and ac spatial distributions of the junction phases and induced circulating currents. We also estimate the interval of the driving current in which a given RS state is stable. All these analytical predictions compare well with our numerics. We then combine these results to deduce the parameter region ͑in the damping coefficient vs magnetic-field plane͒ where RS states cannot exist.

Broken Symmetry of Row Switching in 2D Josephson Junction Arrays

“…For underdamped junctions, these states manifest themselves by various branches on the current-voltage (I-V ) characteristics. The hysteretic switching between branches has been found in stacks of Josephson tunnel junctions [4], layered high-temperature superconductors [5] and twodimensional (2D) Josephson junction arrays [2,3,7,8].In 2D arrays, this switching effect appears in the form of row switching when a voltage drop in array occurs on individual rows of junctions perpendicular to the direction of the bias current. A typical behavior found in both experiments [7] and in numerical simulations [3,9] is that the number of rows switched to resistive state and, even more important, their distribution inside the array can change during sweeping the I-V curve.…”

“…For underdamped junctions, these states manifest themselves by various branches on the current-voltage (I-V ) characteristics. The hysteretic switching between branches has been found in stacks of Josephson tunnel junctions [4], layered high-temperature superconductors [5] and twodimensional (2D) Josephson junction arrays [2,3,7,8].…”

“…All arrays are underdamped and typical values of the McCumber parameter [12] β c at T = 4.2 K are around 200. The parameter β L characterizing the influence of self-inductance [6,8] changes from β L ≃ 0.5 for triangular arrays to β L ≃ 2 for square arrays. The bias current I is injected uniformly via external resistors.…”

Transitions in two sinusoidally coupled Josephson junction rotators

“…The abundant nonlinear properties embodied in this model is studied intensively [2][3][4][5][6][7][8][9].…”

Phase-locking of disordered two-dimensional Josephson junction arrays to microwave radiation

“…For instance in a recent experiment [13] it has shown that individual rows seem capable to phase-lock, so that the whole system is better described in terms of oscillators constituted by rows than by considering the individual junctions as elementary oscillators. Also in theoretical investigations, such as those of Barahona and Watanabe [14], the motion of°uxons across the arrays, in absence of microwave excitations, has been handled starting from the dynamics of the elementary rows.…”