Abstract:
We study the low-temperature properties of linear Josephson-junction arrays capacitively coupled to a proximate two-dimensional diffusive metal. Using bosonization techniques, we derive an effective model for the array and obtain its critical properties and phases at T = 0 using a renormalization group analysis and a variational approach. While static screening effects given by the presence of the metal can be absorbed in a renormalization of the parameters of the array, backscattering originated in the dynamically screened Coulomb interaction produces a non-trivial stabilization of the insulating groundstate and can drive a superconductor-insulator transition. We study the consequences for the transport properties in the low-temperature regime. In particular, we calculate the resisitivity as a function of the temperature and the parameters of the array, and obtain clear signatures of a superconductor-insulator transition that could be observed in experiments.

Abstract:
We propose a mechanism of coherent emission from driven vortices in stacked intrinsic Josephson junctions. In contrast to super-radiance, which occurs only for highly ordered vortex lattices, we predict resonant radiation emission from weakly correlated vortex arrays. Our analytical results for the THz wave intensity, resonance frequencies, and the dependence of THz emission power on dissipation are in good agreement with the ones obtained by recent simulations.

Abstract:
By introducing a realistic model of nanogranular superconductors (NGS) based on 2D arrays of Josephson nanocontacts (created by a network of twin-boundary dislocations with strain fields acting as insulating barriers between hole-rich domains), in this Chapter we present some novel phenomena related to mechanical, magnetic, electric and transport properties of NGS in underdoped single crystals. In particular, we consider chemically induced magnetoelectric effects and flux driven temperature oscillations of thermal expansion coefficient. We also predict a giant enhancement of the nonlinear thermal conductivity of NGS reaching up to 500% when the intrinsically induced chemoelectric field (created by the gradient of the chemical potential due to segregation of hole producing oxygen vacancies) closely matches the externally produced thermoelectric field. The estimates of the model parameters suggest quite an optimistic possibility to experimentally realize these promising and important for applications effects in non-stoichiometric NGS and artificially prepared arrays of Josephson nanocontacts.

Abstract:
We have studied the magnetic-field-driven quantum phase transitions in Josephson junction arrays with a large coordination number. The characteristic energies were extracted in both the superconducting and insulating phases by integrating the current-voltage characteristics over a voltage range 2eV\leqk_B T. For the arrays with a relatively strong Josephson coupling, we observed duality between the energies in the superconducting and insulating phases. The arrays with a weaker Josephson coupling demonstrate an intermediate, "bad metal" regime in weak magnetic fields; this observation underlines the importance of vortex pinning at large scales and, presumably, emergent inhomogeneity in the presence of strong offset charge disorder.

Abstract:
A comparative study of the magnetic properties of shunted and unshunted two-dimensional Josephson junction arrays (2D-JJA) is presented. Using a single-plaquette approximation of the 2D-JJA model, we were able to successfully fit all our experimental data (for the temperature, AC and DC field dependencies of susceptibility) and demonstrate that the dynamic reentrance of AC susceptibility is directly linked to the value of the Stewart-McCumber parameter \beta_C. Based on extensive numerical simulations, a phase diagram \beta_C vs \beta_L is plotted which demarcates the border between the reentrant and non-reentrant behavior in the arrays.

Abstract:
we have shown that the paramagnetic meissner effect (pme) is directly associated with pinning, and not necessarily related to the presence of p-junctions. through the study of the magnetic properties of two-dimensional josephson junction arrays (2d-jja) in the present work we show that, among the systems exhibiting pme, only those with suffciently low dissipation and high capacitance will show dynamics reentrance. the concept of a critical state and its use in the interpretation of ac magnetization data in terms of a critical current density were introduced to derive the magnetic properties of hard type-ii superconductors. in the critical state model proposed by bean, flux lines penetrate into the sample and, due to the presence of disorder they give rise to a steady flux gradient. here we show that in 2d-jja this typical picture is valid only in short-range distances. for long-range distances, the picture of uniform flux fronts, as described by a critical state model, breaks down and the penetration of the magnetic field takes place through the growth of magnetic dendrites. de gennes originally compared the slope of a pile of vortices to a sand-pile, with the slope being proportional to the local magnitude of the critical current. dynamical properties of the sand-pile problem have attracted new attention since it consists of a marginally stable system displaying self-organized criticality (soc). in this case, when a superconductor is in the bean critical state, the addition of vortices occurs by increasing the external magnetic field. this procedure is analogous to the introduction of new grains to a sand-pile and is expected to produce an avalanche of grains of sand (or, equivalently, vortices) of all sizes to maintain a constant gradient in the grain (or, magnetic ux) density. we show in this work strong evidences pointing out that, for some specific conditions, magnetic field penetrates 2d-jja in ux avalanches.

Abstract:
We have shown that the Paramagnetic Meissner Effect (PME) is directly associated with pinning, and not necessarily related to the presence of pi-junctions. Through the study of the magnetic properties of two-dimensional Josephson junction arrays (2D-JJA) in the present work we show that, among the systems exhibiting PME, only those with suffciently low dissipation and high capacitance will show dynamics reentrance. The concept of a critical state and its use in the interpretation of AC magnetization data in terms of a critical current density were introduced to derive the magnetic properties of hard type-II superconductors. In the critical state model proposed by Bean, flux lines penetrate into the sample and, due to the presence of disorder they give rise to a steady flux gradient. Here we show that in 2D-JJA this typical picture is valid only in short-range distances. For long-range distances, the picture of uniform flux fronts, as described by a critical state model, breaks down and the penetration of the magnetic field takes place through the growth of magnetic dendrites. De Gennes originally compared the slope of a pile of vortices to a sand-pile, with the slope being proportional to the local magnitude of the critical current. Dynamical properties of the sand-pile problem have attracted new attention since it consists of a marginally stable system displaying self-organized criticality (SOC). In this case, when a superconductor is in the Bean critical state, the addition of vortices occurs by increasing the external magnetic field. This procedure is analogous to the introduction of new grains to a sand-pile and is expected to produce an avalanche of grains of sand (or, equivalently, vortices) of all sizes to maintain a constant gradient in the grain (or, magnetic ux) density. We show in this work strong evidences pointing out that, for some specific conditions, magnetic field penetrates 2D-JJA in ux avalanches.

Abstract:
We study the quantum phase transitions in two-dimensional arrays of Josephson-couples junctions with short range Josephson couplings (given by the Josephson energy) and the charging energy. We map the problem onto the solvable quantum generalization of the spherical model that improves over the mean-field theory method. The arrays are placed on the top of a two-dimensional electron gas separated by an insulator. We include effects of the local dissipation in the presence of an external magnetic flux f in square lattice for several rational fluxes f=0,1/2,1/3,1/4 and 1/6. We also have examined the T=0 superconducting-insulator phase boundary as function of a dissipation alpha for two different geometry of the lattice: square and triangular. We have found critical value of the dissipation parameter independent on geometry of the lattice and presence magnetic field.

Abstract:
The form of the fluctuation-dissipation theorem for a resistively shunted Josephson juction array is derived with the help of the method which explicitely takes into acoount screening effects. This result is used to express the flux noise power spectrum in terms of frequency dependent sheet impedance of the array. The relation between noise amplitude and parameters of the detection coil is analysed for the simplest case of a single-loop coil.

Abstract:
We present an experimental and theoretical study of row switching in two-dimensional Josephson junction arrays. We have observed novel dynamic states with peculiar percolative patterns of the voltage drop inside the arrays. These states were directly visualized using laser scanning microscopy and manifested by fine branching in the current-voltage characteristics of the arrays. Numerical simulations show that such percolative patterns have an intrinsic origin and occur independently of positional disorder. We argue that the appearance of these dynamic states is due to the presence of various metastable superconducting states in arrays.