We have studied phase transitions in fabricated 2D arrays of Josephson junctions where the charging and Josephson coupling energies are about equal. We find a crossover from superconducting behavior in low fields to insulating behavior for fields above a critical value of 0.1-0.2 flux quanta per unit cell. The quantitative aspects agree well with predictions from a recent theory for quantum vortex motion by M. P. A. Fisher and with measurements on films. Similar transitions are found around values /=/i/m, where/is the flux per cell and «,w = 1,2,3. The field dependence is periodic in/with period 1.

Vortex motion has been studied for the first time in high-quality, highly underdamped, twodimensional Josephson-junction arrays, with normal-state junction resistances ranging from 43 n to 48 kn. Strong similarity is found with the dynamics of the phase in single junctions, e.g., vortices with mass moving in the spatially periodic washboard potential of the 2D array. High-resistance arrays show resistance below 35 mK due to either thermally activated depinning or quantum fluctuations.PACS numbers: 74.50.+r, 74.60.Ge, 74.60.Jg Fabricated two-dimensional Josephson-junction arrays are model systems for the study of vortex motion in 2D superconductors, where parameters are well known and can be varied over orders of magnitude. So far, experimental studies of arrays have been concentrated on overdamped junctions and viscous vortex flow. Vortex dynamics in systems with low dissipation is very interesting from a theoretical point of view, and its understanding may be very relevant for the interpretation of experimental data on high-resistance superconducting films. Theoretical predictions have been made for the quantum behavior of vortices, 1 " 4 ballistic motion, 3 ' 5 and AharonovCasher oscillations of quantum vortices moving in a ring around charge. 6 Superconductor-insulator transitions occur as a function of the ratio of charging energy versus Josephson coupling energy, 7,8 and as a function of magnetic field. 9 Vortex dynamics near those transitions are of special interest. In this paper we present the first experimental data on vortices in arrays of high-quality strongly underdamped aluminum tunnel junctions, which we see as the necessary first steps towards studies of the fascinating predicted effects. We find that the whole picture of vortex motion in the array is closely analogous to the dynamics of the phase in single underdamped Josephson junctions.In underdamped arrays, the junction capacitance leads to a mass term in the equation of motion. A vortex moving with velocity u produces a voltage across a junction F = (Oo/2;r)0, where o is the flux quantum and 0 is the phase difference with a time rate of change proportional to u.

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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.