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We investigate analytically and numerically the mean-fieldsuperconducting-normal phase boundaries of two-dimensional superconducting wirenetworks and Josephson junction arrays immersed in a transverse magnetic field.The geometries we consider include square, honeycomb, triangular, and kagome'lattices. Our approach is based on an analytical study of multiple-loopAharonov-Bohm effects: the quantum interference between different electronclosed paths where each one of them encloses a net magnetic flux. Specifically,we compute exactly the sums of magnetic phase factors, i.e., the lattice pathintegrals, on all closed lattice paths of different lengths. A very largenumber, e.g., up to $10^{81}$ for the square lattice, exact lattice pathintegrals are obtained. Analytic results of these lattice path integrals thenenable us to obtain the resistive transition temperature as a continuousfunction of the field. In particular, we can analyze measurable effects on thesuperconducting transition temperature, $T_c(B)$, as a function of the magneticfiled $B$, originating from electron trajectories over loops of variouslengths. In addition to systematically deriving previously observed features,and understanding the physical origin of the dips in $T_c(B)$ as a result ofmultiple-loop quantum interference effects, we also find novel results. Inparticular, we explicitly derive the self-similarity in the phase diagram ofsquare networks. Our approach allows us to analyze the complex structurepresent in the phase boundaries from the viewpoint of quantum interferenceeffects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure

physical review. b, condensed matter

Quantum interference in superconducting wire networks and Josephson junction arrays: An analytical approach based on multiple-loop Aharonov-Bohm Feynman path integrals