Topological order in the insulating Josephson junction array

TL;DR

This paper introduces a Josephson junction array that can be tuned into a topologically ordered insulating state with protected ground state degeneracy, demonstrating potential for robust quantum states.

Contribution

It proposes a novel Josephson junction array exhibiting topological order and analyzes its properties, including ground state degeneracy and energy gaps, under external magnetic tuning.

Findings

Array exhibits a topologically protected ground state degeneracy.

The insulating state maintains a gap to half vortices.

External magnetic field tuning enables control over the topological phase.

Abstract

We propose a Josephson junction array which can be tuned into an unconventional insulating state by varying external magnetic field. This insulating state retains a gap to half vortices; as a consequence, such array with non-trivial global geometry exhibits a ground state degeneracy. This degeneracy is protected from the effects of external noise. We compute the gaps separating higher energy states from the degenerate ground state and we discuss experiments probing the unusual properties of this insulator.