Crossover from bias-induced to field-induced breakdown in one-dimensional band and Mott insulators attached to electrodes

Nonequilibrium states induced by an applied bias voltage (V) and the corresponding current-voltage characteristics of one-dimensional models describing band and Mott insulators are investigated theoretically by using nonequilibrium Green's functions. We attach the models to metallic electrodes, the effects of which are incorporated into the self-energy. Modulation of the electron density and the scalar potential coming from the additional long-range interaction are calculated self-consistently within the Hartree approximation. For both models of band and Mott insulators with length L_C, the bias voltage induces a breakdown of the insulating state, the threshold of which shows a crossover depending on L_C. It is determined basically by the bias V_thΔ for L_C smaller than the correlation length ξ=W/Δ, where W denotes the bandwidth and Δ denotes the energy gap. For systems with L_Cξ, the threshold is governed by the electric field V_th/L_C, which is consistent with a Landau-Zener-type breakdown V_th/L_C Δ2/W. We demonstrate that the spatial dependence of the scalar potential is crucially important for this crossover by showing the case without the scalar potential, where the breakdown occurs at V_thΔ regardless of the length L_C.