Josephson junction chains with long-range interactions: Phase slip proliferation versus Kosterlitz-Thouless transition

Abstract

The role of long-range badly screened Coulomb interactions in a one-dimensional chain of Josephson junctions is studied. Correlation functions for the phase correlator are obtained as a function of the Josephson coupling energy, the short-range part of the Coulomb repulsion, and its long-range component. Although quasi-long-range order is no longer possible and the usual Kosterlitz-Thouless transition no longer exists, there are remnants of it. As an application, we calculate the $I\ensuremath{-}V$ curves for Andreev reflection when a normal metal is placed in contact with the chain. Formally, there is always an offset voltage ${V}_{0}$ below which no current can flow; however, in some regimes ${V}_{0}$ can be negligible. Contrary to what happens without long-range interactions, the Andreev current, as a function of applied voltage, increases faster than any power law. Signatures of long-range interactions and phase slips appear in the $I\ensuremath{-}V$ curves. A possible application for quasi-one-dimensional thin superconducting wires is outlined.