Classical and quantum properties of variable-coordination number Josephson junction arrays

Josephson junction arrays are a quintessential platform which has been widely used in the study a wide range of problems in classical and quantum dynamics. In this thesis, we introduce a Josephson lattice with a new topology which allows the adjustment of the coordination number. For large coordination numbers, the lattice is amenable to mean field predictions. We have employed this lattice to study classical phase transitions. The lattice has been studied by Monte-Carlo simulations to determine TC. The experimental determination of TC agrees with numerical studies and are close to the mean field predictions. We have also studied the magnetic field dependence of the transition temperatures using a tight-binding model. The experimental results agree fairly well with the results of numerical calculations. The classical dynamics of this lattice has been simulated with RCSJ model and are compared with the switching dynamics of the array.;We have studied both zero field and field-tuned quantum phase transitions the VZN lattice. The zero-field transition occurs at a critical value of the control parameter g smaller than the disorder-free case. When frustrated by the magnetic field, the arrays demonstrated several quantum phase transitions at different critical values of the resistance between RC = 3--10kO, which is in line with earlier observations. In particular, with increasing B we observed transitions between three states: a) the superconducting state with zero R, b) the metallic state with a weak R dependence on T in the range 0.05 K < T < 0.2K, and c) the insulating state with an activation dependent R( T). From studies of magnetic field dependences of T C(f), we can state that the origin of the intermediate metallic state is due to the vortex liquid phase. In this sense, we do not observe the intermediate metallic state observed in all prior experiments on 2D Josephson arrays. The activation energy, extracted from the current-voltage characteristics and the Arrhenius fitting of R(T ) in the insulating regime, has been studied as a function of the temperature and the magnetic field. This data together with a suppressed critical point suggest the possible development of a strongly inhomogeneous state in the vicinity of the superconducting-to-insulating transition.