Nonequilibrium restoration of duality symmetry in the vicinity of the superconductor-to-insulator transition

The magnetic field driven superconductor to insulator transition in thin films was theoretically analyzed via a vortex-charge duality transformation applied to the Hamiltonian. Vortices condensation was conjectured as the underline physical mechanism of the insulating phase. Experimental evidence supported duality symmetry across the magnetic-field driven superconductor to insulator transition in amorphous Indium Oxide films. Counterintuitively, duality symmetry is broken at low temperatures where the insulating phase develops strongly non linear current-voltage characteristics. Here, we follow the breakdown of duality symmetry down to very low temperatures and demonstrate the restoration of duality symmetry out of equilibrium.