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

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 Coulomb repulsion and its long range component. Though 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 $I-V$ curves for Andreev reflexion 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 $I-V$ curves. Possible application for quasi one-dimensional thin superconducting wires is outlined.