Ballistic Vortices in Josephson-Junction Arrays

Abstract

We have observed ballistic motion of vortices in arrays of superconducting tunnel junctions. In a special geometry vortices are accelerated in one region, then launched into a second region without driving forces. At low temperatures, where damping is small, the vortices are found to propagate in a beam across the force-free region.Research on vortex dynamics in two-dimensional superconductors has so far concentrated on systems where, apart from driving forces, only pinning potentials and viscous damping are important. Recently [l-41, attention has been drawn to the opposite and novel regime of vortex dynamics in systems with low dissipation. Here, the vortex velocity is high enough so that the energy stored in the electric field generated by the vortex has to be taken into account. This contribution to the energy can be viewed as a kinetic-energy term and defines an effective vortex mass, which is proportional to the junction capacitance [l-31. Theoretical predictions have been made for ballistic motion of vortices [3,5] and quantum behaviour of vortices [2,5-71. Particularly well suited for studies of the dynamics of mass-carrying vortices are 2D arrays of superconducting islands connected by underdamped Josephson tunnel junctions. Josephson-junction arrays have the advantage that parameters are well known, can be varied over orders of magnitude and that networks can be made in every desired geometry. Recent experiments [8,9] on vortex motion in underdamped Josephson-junction arrays clearly demonstrate the existence of a mass term in the equation of motion. For a square array with cell area S, the value of the vortex mass M , following from a quasi-static approach [l-31 is M , = @C/(2S), where C is the junction capacitance and Q0 the flux quantum. Recent theoretical calculations [7] indicate that the effective vortex mass of a moving vortex can be larger by almost an order of magnitude.

Magnetic Monopoles and Superinsulation in Josephson Junction Arrays

“…It is also known that dissipation is substantially reduced when the Coulomb interaction becomes long-range [32], exactly the regime we are interested in. Finally, ballistic motion of vortices has indeed been observed experimentally [33]. This calls for the necessity of adding a vortex kinetic term to the action.…”

Topological Gauge Theory of Josephson Junction Arrays: The Discovery of Superinsulation

“…They can be thought of as half-lines of simultaneous phase slips of opposite chirality, which end on the island between the two adjacent plaquettes. Ballistic vortex motion corresponding to vortex tunneling from one plaquette to the other has actually been experimentally observed in [36]. The kinetic term for vortices involves the time derivative of a i , (∆ 0 a i ) 2 .…”

Topological Gauge Theory of Josephson Junction Arrays: The Discovery of Superinsulation

“…They can be seen as half-lines of simultaneous phase slips of opposite chirality, which end in the island between the two adjacent plaquettes. Ballistic vortex motion, represented by phase slips corresponding to one vortex tunneling from one plaquette to the other, has actually been exeperimentally observed in [36]. The kinetic term for vortices will involve the time derivative of a i , (∆ 0 a i ) 2 .…”