Vortices and plasmons in inductive periodic Josephson-junction arrays

We derive a Hamiltonian for two- and three-dimensional inductive Josephson-junction arrays. The variables to describe the system are the gauge-invariant phase differences across the junctions. Therefore in this approach the phase of the superconducting order parameter and the magnetic vector potential are treated on equal footing, which makes it a useful tool to study phenomena in which fluctuations of both magnetic field and the superconducting order parameter are relevant. Among such applications is the study of thermodynamics of the mixed state of high-T-c superconductors at flux densities B much less than H-c2. We take into account screening by the superconducting currents in the electrodes forming the network and show that their effect in two-dimensional networks is only important at distances smaller than some characteristic length Lambda(e). In three-dimensional networks the magnetic interaction of currents is always short ranged regardless of the superconducting properties of the electrodes. We also derive time-dependent equations for the phase differences and a dispersion relation of a plasmon at zero temperature in the absence of vortices.