Interplay of classical and quantum capacitance in a one-dimensional array of Josephson junctions

Abstract

Even in the absence of Coulomb interactions, phase fluctuations induced by quantum size effects become increasingly important in superconducting nanostructures as the mean level spacing becomes comparable with the bulk superconducting gap. Here we study the role of these fluctuations, termed “quantum capacitance,” in the phase diagram of a one-dimensional ring of ultrasmall Josephson junctions at zero temperature by using path-integral techniques. Our analysis also includes dissipation due to quasiparticle tunneling and Coulomb interactions through a finite mutual and self-capacitance. The resulting phase diagram has several interesting features: A finite quantum capacitance can stabilize superconductivity even in the limit of only a finite mutual-capacitance energy, which classically leads to breaking of phase coherence. In the case of vanishing charging effects, relevant in cold-atom settings where Coulomb interactions are absent, we show analytically that superfluidity is robust to small quantum finite-size fluctuations and identify the minimum grain size for phase coherence to exist in the array. We have also found that the renormalization group results are in some cases very sensitive to relatively small changes of the instanton fugacity. For instance, a certain combination of capacitances could lead to a nonmonotonic dependence of the superconductor-insulator transition on the Josephson coupling.

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