Superinsulation, electric confinement in condensed matter

Superinsulation is the confining phase of condensed matter systems. It is a genuine quantum state of matter, dual to superconductivity, just as confinement in particle physics is dual to the Higgs phase. In contrast to hadron physics, the gauge field that becomes confining is not colour SU(3) but the conventional U(1) electromagnetic field. Superinsulation arises in superconductors with an emergent granular condensate when core-less XY vortices between condensate grains become tensionless, unobservable Dirac strings and magnetic monopoles are liberated and condense. This magnetic condensate confines electric fields into flux tubes, strings that generate a linear potential between Cooper pairs. These dual Abrikosov flux tubes give rise to infinite electrical resistance, persisting up to a finite deconfinement temperature. We shall review the theoretical framework of superinsulation together with its experimental validation, including the direct observation of the linear confining potential and we shall stress how phase-only approaches and disorder-based ideas for the phases around the superconductor-to-insulator transition are hard to reconcile with recent experimental observations.