Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature , the maximum of the condensation energy as a function of doping, the correlation between maximum and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.

Many correlated systems feature an insulator-to-metal transition that can be triggered by an electric field. Although it is known that metallization takes place through filament formation, the details of how this process initiates and evolves remain elusive. We use in-operando optical reflectivity to capture the growth dynamics of the metallic phase with space and time resolution. We demonstrate that filament formation is triggered by nucleation at hotspots, with a subsequent expansion over several decades in time. By comparing three case studies (VO2, V3O5 and V2O3), we identify the resistivity change across the transition as the crucial parameter governing this process. Our results provide a spatiotemporal characterization of volatile resistive switching in Mott insulators, key for emerging technologies such as optoelectronics or neuromorphic computing.