Nonlinear transport in the one dimensional Hubbard model at half-filling under a finite bias voltage is investigated by the adaptive time-dependent density matrix renormalization group method. For repulsive on-site interaction, dielectric breakdown of the Mott insulating ground state to a current-carrying nonequilibrium steady state is clearly observed when the voltage exceeds the charge gap. It is found that by increasing the voltage further the current-voltage characteristics are scaled only by the charge gap and the scaling curve exhibits almost linear dependence on the voltage whose slope is suppressed by the electron correlation. In the case of attractive interaction the linear conductance is the perfect one
2e2/h which agrees with the prediction by the Luttinger liquid theory.
We calculate the nonequilibrium electronic transport properties of a one-dimensional interacting chain at half filling, coupled to noninteracting leads. The interacting chain is initially in a Mott insulator state that is driven out of equilibrium by applying a strong bias voltage between the leads. For bias voltages above a certain threshold we observe the breakdown of the Mott insulator state and the establishment of a steady-state electronic current through the system. Based on extensive time-dependent density-matrix renormalization-group simulations, we show that this steady-state current always has the same functional dependence on voltage, independent of the microscopic details of the model and we relate the value of the threshold to the Lieb-Wu gap. We frame our results in terms of the Landau-Zener dielectric breakdown picture. Finally, we also discuss the real-time evolution of the current, and characterize the current-carrying state resulting from the breakdown of the Mott insulator by computing the double occupancy, the spin structure factor, and the entanglement entropy.
Nonlinear response of a Mott insulator to external electric field, corresponding to dielectric breakdown phenomenon, is studied within of a one-dimensional half-filled Hubbard model. It is shown that in the limit of nearly spin-polarized insulator the decay rate of the ground state into excited holon-doublon pair can be evaluated numerically as well to high accuracy analytically. Results show that the threshold field depends on the charge gap as F(th)∝Δ(3/2). Numerical results on small systems indicate on the persistence of a similar mechanism for the breakdown for decreasing magnetization down to unpolarized system.
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.
We study the nonequilibrium steady state of a Mott insulator coupled to a thermostat and driven by a constant electric field, starting from weak fields, until the dielectric breakdown, and beyond. We find that the conventional Zener picture does not describe the steady-state physics. In particular, the current at weak field is found to be controlled by the dissipation. Moreover, in connection with the electric-field-driven dimensional crossover, we find that the dielectric breakdown occurs when the field strength is on the order of the Mott gap of the corresponding lower-dimensional system. We also report a resonance and the meltdown of the quasiparticle peak when the field strength is half of this Mott gap.
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 ${V}_{\mathrm{th}}~\ensuremath{\Delta}$ for
LC smaller than the correlation length $\ensuremath{\xi}=W/\ensuremath{\Delta}$, where
W denotes the bandwidth and $\ensuremath{\Delta}$ denotes the energy gap. For systems with ${L}_{C}\ensuremath{\gg}\ensuremath{\xi}$, the threshold is governed by the electric field
Vth/LC, which is consistent with a Landau-Zener--type breakdown ${V}_{\mathrm{th}}/{L}_{C}\ensuremath{\propto}{\ensuremath{\Delta}}^{2}/W$. 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 ${V}_{\mathrm{th}}~\ensuremath{\Delta}$ regardless of the length
LC.