Magnetic Monopoles and Superinsulation in Josephson Junction Arrays

Carlo Trugenberger,M. Cristina Diamantini,Nicola Poccia,Flavio S. Nogueira,Valerii M. Vinokur

doi:10.3390/quantum2030027

Abstract

Electric-magnetic duality or S-duality, extending the symmetry of Maxwell’s equations by including the symmetry between Noether electric charges and topological magnetic monopoles, is one of the most fundamental concepts of modern physics. In two-dimensional systems harboring Cooper pairs, S-duality manifests in the emergence of superinsulation, a state dual to superconductivity, which exhibits an infinite resistance at finite temperatures. The mechanism behind this infinite resistance is the linear charge confinement by a magnetic monopole plasma. This plasma constricts electric field lines connecting the charge–anti-charge pairs into electric strings, in analogy to quarks within hadrons. However, the origin of the monopole plasma remains an open question. Here, we consider a two-dimensional Josephson junction array (JJA) and reveal that the magnetic monopole plasma arises as quantum instantons, thus establishing the underlying mechanism of superinsulation as two-dimensional quantum tunneling events. We calculate the string tension and the dimension of an electric pion determining the minimal size of a system capable of hosting superinsulation. Our findings pave the way for study of fundamental S-duality in desktop experiments on JJA and superconducting films.

Highlights

The superinsulating state, dual to superconductivity [1,2,3,4,5,6,7], is a remarkable manifestation of S-duality [8] in condensed matter physics
The configuration space of the theory of vortices decomposes into so-called superselection sectors, characterized by the integer total vortex number, which are connected via instantons, non-perturbative configurations representing quantum tunneling events between topological vacua [17]
In two spatial dimensions (2D), these instantons are nothing but magnetic monopoles [18]

Summary

Introduction

The superinsulating state, dual to superconductivity [1,2,3,4,5,6,7], is a remarkable manifestation of S-duality [8] in condensed matter physics. A drastically different class of phenomena arises if monopoles form a monopole plasma as a result of multiple instanton quantum tunneling events In this case, a monopole plasma offers an ideal screening mechanism for electric fields, and the system harboring the monopole plasma makes a perfect dielectric with zero static dielectric constant, ε = 0, as long as the electric field does not exceed some threshold value [13]. As the perfect diamagnetism is associated with an infinite conductance, i.e., superconductivity, the perfect dielectricity should correspond to dual superconductors possessing an infinite resistance, i.e., superinsulators [1,5]

Methods

Results

Conclusion