Vortex dynamics in classical Josephson junction arrays: models and recent experimental developments

Abstract

This review deals with the recent progress achieved in the understanding of vortex dynamics in discrete arrays of classical Josephson junctions, JJAs. We first give an up-to-date overview of the discrete models currently used to describe the physics of JJAs: the `JJ array formalism', the discretized version of the sine-Gordon equation and the Frenkel-Kontorova model. Special emphasis is put on the recent reformulation of the screening term that makes use of the full-inductance matrix. The relationship between the phase and the vortex-particle dynamics is also discussed. An overview of the `state of the art' in the understanding of the single-vortex dynamics in overdamped JJAs follows; the dependence of the motion of the vortex on its size (i.e. on the screening strength, the sample geometry and the coupling anisotropy, ) and, also, on the bias current is pointed out and discussed. A peculiar phenomenon, alternate-vortex motion, is also briefly illustrated. Subsequently, we review the single-vortex dynamics in underdamped JJAs. A short description of the conditions that lead to the observation of anomalous dissipation, vortex reflection, ballistic vortex motion, resonances, instabilities and row switching is given. To conclude, we discuss open problems and future perspectives of the research on JJAs.

Static properties of classical Josephson junction arrays: models and experimental achievements

“…F F p;q is a form factor matrix related to the geometry of the array. Details of its computation can be found in [8]. Fluxoid quantization can be expressed as…”

“…In the recent past we have already devoted a review and a tutorial paper to the dynamical properties of a single vortex and to those of the ensembles of locked vortices [8]. Here, instead, we intend to give a (necessarily very simplified) overview of some recent works on the static properties of the arrays.…”

Millimetre and sub-mm wavelength radiation sources based on discrete Josephson junction arrays

“…To operate the array in the flux-flow regime, underdamped junctions are required. This was the subject of several investigations [23][24][25][26]. Although this type of device is extremely interesting for the investigation of the complex dynamics connected with fluxon movement in discrete systems, direct radiation measurements are not available.…”

Rectification and phase locking of graphite

“…The properties of Shapiro steps [1,2] have been studied experimentally and theoretically for many years in the dissipative dynamics of many-body systems, such as charge-density or spin-density wave conductors [3][4][5][6][7], vortex lattices [8][9][10][11][12][13], colloids [14,15] and Josephsonjunction arrays (JJA) biased by external currents [16][17][18][19][20]. To understand these very complex physical systems, the focus was always on simple many-body models.…”