Superinsulator-Superconductor Duality in Two Dimensions

TL;DR

This paper reveals a duality between superconductivity and superinsulation in two-dimensional systems, based on symmetry principles, and demonstrates their coexistence and transitions in Josephson junction arrays and disordered films.

Contribution

It introduces the concept of superinsulation as a dual state to superconductivity, grounded in the Heisenberg uncertainty principle, and links this duality to BKT transitions in various 2D systems.

Findings

Superinsulation arises as a dual to superconductivity in 2D systems.

The vortex-charge-BKT transition duality explains superinsulation in Josephson junction arrays.

Disordered films near the transition exhibit Coulomb interactions leading to superinsulation.

Abstract

For nearly a half century the dominant orthodoxy has been that the only effect of the Cooper pairing is the state with zero resistivity at finite temperatures, superconductivity. In this work we demonstrate that by the symmetry of the Heisenberg uncertainty principle relating the amplitude and phase of the superconducting order parameter, Cooper pairing can generate the dual state with zero conductivity in the finite temperature range, superinsulation. We show that this duality realizes in the planar Josephson junction arrays (JJA) via the duality between the Berezinskii-Kosterlitz-Thouless (BKT) transition in the vortex-antivortex plasma, resulting in phase-coherent superconductivity below the transition temperature, and the charge-BKT transition occurring in the insulating state of JJA and marking formation of the low-temperature charge-BKT state, superinsulation. We find that in disordered superconducting films that are on the brink of superconductor-insulator transition the Coulomb forces between the charges acquire two-dimensional character, i.e. the corresponding interaction energy depends logarithmically upon charge separation, bringing the same vortex-charge-BKT transition duality, and realization of superinsulation in disordered films as the low-temperature charge-BKT state. Finally, we discuss possible applications and utilizations of superconductivity-superinsulation duality.