Crossover from bias-induced to field-induced breakdowns 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 whose effects 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, whose threshold shows a crossover depending on L_C. It is determined basically by the bias $V_{th}\sim \Delta$ for L_C smaller than the correlation length $\xi=W/\Delta$ where W denotes the bandwidth and $\Delta$ the energy gap. For systems with $L_C\gg \xi$, the threshold is governed by the electric field, $V_{th}/L_C$, which is consistent with a Landau-Zener-type breakdown, $V_{th}/L_C\propto \Delta^2/W$. 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 $V_{th}\sim \Delta$ regardless of the length L_C. 
Yasuhiro Tanaka, Kenji Yonemitsu
cond-mat.str-el