Abstract
We review the topological gauge theory description of Josephson junction arrays (JJA), fabricated systems which exhibit the superconductor-to-insulator transition (SIT). This description revealed the topological nature of the phases around the SIT and led to the discovery of a new state of matter, the superinsulator, characterized by infinite resistance, even at finite temperatures, due to linear confinement of electric charges. This discovery is particularly relevant for the physics of superconducting films with emergent granularity, which are modeled with JJAs and share the same phase diagram.
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