Role of Goldstone mode in nonequilibrium insulator under DC electric field

Measurements of resistive breakdown in electronic systems under a DC electric field have shown that the threshold fields for the insulator-to-metal transition are significantly lower than predicted by single-electron excitation scenarios, such as the Landau-Zener theory. In this work, we propose an alternate mechanism of destabilizing ordered insulators under a DC electric field by fluctuations of the order parameters through the Goldstone mode excitation. The low-energy bosonic excitations receive energy from accelerated electrons and thus destroy the spontaneous symmetry breaking. Using the Keldysh Gree's function formalism, we numerically confirm that the Goldstone mode remains well-defined in the nonequilibrium steady state, while its nonequilibrium excitations are sensitive to the electric field. The effective temperature of the Goldstone mode increases much more rapidly than the electronic effective temperature, with the bosonic threshold field significantly smaller than the electronic one, which suggests that collective phase dynamics may further reduce the transition field to the experimental range via a purely electronic mechanism.