The current-voltage characteristics and mechanism of bias-induced breakdown in one-dimensional models for 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. For the models of both the band and the Mott insulators with lengths L C, the bias voltage induces a breakdown of the insulating state, and the breakdown mechanism shows a crossover depending on L C. When L C is smaller than the correlation length ξ = W/Δ, the threshold is determined basically by the bias V th ∼ Δ, where W and Δ are the bandwidth and the energy gap, respectively. For systems with L C ≫ ξ, 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.
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