Nonequilibrium mean-field theory of resistive phase transitions

We investigate the quantum mechanical origin of resistive phase transitions in solids driven by a constant electric field in the vicinity of a metal-insulator transition. We perform a nonequilibrium mean-field analysis of a driven-dissipative symmetry-broken insulator, which we solve analytically for the most part. We find that the insulator-to-metal transition (IMT) and the metal-to-insulator transition (MIT) proceed by two distinct electronic mechanisms: Landau-Zener processes and the destabilization of the metallic state by Joule heating, respectively. However, we show that both regimes can be unified in a common effective thermal description, where the effective temperature Teff depends on the state of the system. This explains recent experimental measurements in which the hot-electron temperature at the IMT was found to match the equilibrium transition temperature. Our analytic approach enables us to formulate testable predictions on the nonanalytic behavior of I−V relation near the insulator-to-metal transition. Building on these successes, we propose an effective Ginzburg-Landau theory which paves the way to incorporating spatial fluctuations and to bringing the theory closer to a realistic description of the resistive switchings in correlated materials.