Haldane Gap and Fractional Oscillations in Gated Josephson Arrays

TL;DR

This paper predicts novel quantum effects like fractional oscillations and a Haldane gap in gated Josephson arrays, based on an analogy with the twisted quantum xxz model, and discusses experimental realization.

Contribution

It introduces a theoretical framework linking the xxz model to Josephson arrays, predicting fractional Josephson effects and identifying conditions for a Haldane gap.

Findings

Prediction of fractional AC Josephson frequencies.

Identification of a Haldane gap at moderate anisotropy.

Proposal of experimental parameters for observing effects.

Abstract

An analogy between the twisted quantum xxz model and a gated Josephson junction array is used to predict sharp structure in the critical currents versus gate voltage, and fractional AC Josephson frequencies. We prove selection rules for level crossings which imply fractional periodicities of ground states with varying Aharonov-Bohm flux. Extrapolated numerical diagonalization on ladders, find a Haldane gap at moderate easy-plane anisotropy, with vanishing superfluid stiffness. Physical parameters for experimental realization of these novel effects are proposed.