Intrinsic Resistivity via Quantum Nucleation of Phase Slips in a One-Dimensional Josephson Junction Array

The resistivity of a one-dimensional Josephson junction array at zero temperature is calculated by estimating the nucleation rate of quantum phase slips. We choose a certain collective coordinate which describes the nucleation process and estimate the corresponding effective mass. In the strong coupling regime, where Josephson coupling energy exceeds the charging energy, we calculate the nucleation rate by means of WKB method. Our estimation is in good agreement with recent experimental data. The superconductor-insulator transition point is also discussed. 74.50.+r, 73.40.Gk, 64.60.Qb, 64.60.My Typeset using REVTEX 1 Quantum fluctuations have much influence on the properties of one-dimensional systems at low temperatures. For example, in extremely thin superconducting wires which can be regarded as nearly one-dimensional, the quantum fluctuations of the phase of the order parameter nucleate phase slips, which result in finite resistance at zero temperature [1]. Similar effects are expected for a one-dimensional Josephson junction (1D JJ) array. In a 1D JJ array, the phase difference and charge difference across a junction are canonically conjugate variables, so the charging effect is the origin of the quantum fluctuation of phase. When the system size becomes small and the charging energy large enough, nucleation occur frequently and at some critical point, the quantum phase transition from a phase-coherent (superconducting) state to a charge-ordered (insulating) state occurs. Theoretically, this Superconductor-Insulator (S-I) transition in a 1D JJ array can be understood as some version of Kosterlitz-Thouless transition in a (1+1) dimensional classical spin model, extra dimension being imaginary time [2,3]. Recently, such S-I transition was experimentally investigated in detail with 1D JJ arrays having different numbers of superconducting grains [4]. In that work, the S-I transition was actually observed for each N near the point predicted by Kosterlitz-Thouless theory, and what is also remarkable, it was found that arrays have finite resistance at zero temperature even in the superconducting side. It is probable that these intrinsic resistance in the superconducting side are caused by the quantum nucleation of phase slips, as in the case of thin superconducting wires. In order to confirm this interpretation, we study the quantum nucleation process of a phase slip and calculate the nucleation rate in this Letter. The S-I transition point is also discussed. To begin with, we consider a linear array of N(≫ 1) superconducting grains embedded in an insulator at zero temperature. The grains are assumed to be small compared with bulk coherence length, so that the state of ith grain can be described by a single phase θi and number ni of Cooper pairs on the ith grain. The Euclidean action and Hamiltonian are SE[{ni, θi}] = ∫