Superconductor-insulator duality for the array of Josephson wires

We propose novel model system for the studies of superconductor-insulator transitions, which is a regular lattice, whose each link consists of Josephson-junction chain of $N\gg 1$ junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy $E_J$ large compared to the junctions’s Coulomb energy $E_C$. Exact duality transformation is derived, which transforms the Hamiltonian of the proposed model into a standard Hamiltonian of JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by the parameter $q\approx N^2\exp (-\sqrt{8E_J\mathrm{/}{E}_C})$, with superconductive state corresponding to small $q<q_c$. The values of $q_c$ are calculated for magnetic frustrations $f=0$ and $f=\frac{1}{2}$. Temperature of superconductive transition $T_c(q)$ and $q<q_c$ is estimated for the same values of $f$. In presence of strong random offset charges, the T=0 phase diagram is controlled by the parameter $\bar{q}=q\mathrm{/}\sqrt{N}$; we estimated critical value ${\bar{q}}_c$.