Magnetic and transport dc properties of inductive Josephson-junction arrays

We present an extensive study of the de magnetic and transport properties of inductive Josephson junction arrays at zero temperature. We carry out the analysis using the resistively shunted Josephson junction (RSJ) model plus Faraday's law. We explicitly discuss the gauge invariance of the equations as well as their symmetries. We consider and compare the results of three different models for the corresponding inductance matrix: self-inductance, nearest-neighbor inductance, and full inductance matrix. The importance of carefully considering the boundary conditions for external currents is discussed as well. Heuristic analytic results are derived from linearizing the RSJ plus Faraday's law equations. In particular, we discuss the critical properties of the model and the nature of the vortex-vortex interactions when going from negligible to strong screening regimes. The de properties of the arrays are analyzed as a function of the screening parameter kappa = lambda/a, with lambda the magnetic penetration depth and a the lattice spacing. The weak or extreme type II regime corresponds to kappa much greater than 1, and the strong screening or type I regime to kappa less than or equal to 1. We present results for the calculated magnetization and vortex densities as a function of external magnetic fields for a set of kappa's and lattice sizes. A qualitative change is found between the de magnetic and transport responses of the inductive Josephson arrays when going from the type II to the type I regime.