# Superconductor-insulator duality for the array of Josephson wires

I.V. Protopopov and M.V. Feigel'man

Arxiv ID: 0706.0324•Last updated: 6/1/2022

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 $q \approx N^2 \exp(-\sqrt{8E_J/E_C})$, with superconductive state
corresponding to small $q < q_c $. The values of $q_c$ are calculated for
magnetic frustrations $f= 0$ and $f= \frac12$. 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 $\bar{q} = q/\sqrt{N}$; we estimated critical value
$\bar{q}_c$.

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