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 LC, the bias voltage induces a breakdown of the insulating state, the threshold of which shows a crossover depending on LC. It is determined basically by the bias VthΔ for LC smaller than the correlation length ξ=W/Δ, where W denotes the bandwidth and Δ denotes the energy gap. For systems with LCξ, the threshold is governed by the electric field Vth/LC, which is consistent with a Landau-Zener-type breakdown Vth/LC 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 VthΔ regardless of the length LC.
|Physical Review B - Condensed Matter and Materials Physics
|Published - 2011 2月 28
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