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arXiv:1101.2283 · Physical Review B

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

Yasuhiro Tanaka, Kenji Yonemitsu

Published Feb 28, 2011• 15 citations
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Abstract

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 ${V}_{\mathrm{th}}~\ensuremath{\Delta}$ for ${L}_{C}$ 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 ${V}_{\mathrm{th}}/{L}_{C}$, 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 ${L}_{C}$.

DOI
10.1103/physrevb.83.085113

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Nonequilibrium states induced by an applied bias voltage (V)(V)(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{L}_{C}LC​, the bias voltage induces a breakdown of the insulating state, the threshold of which shows a crossover depending on LC{L}_{C}LC​. It is determined basically by the bias Vth \ensuremathΔ{V}_{\mathrm{th}}~\ensuremath{\Delta}Vth​ \ensuremathΔ for LC{L}_{C}LC​ smaller than the correlation length \ensuremathξ=W/\ensuremathΔ\ensuremath{\xi}=W/\ensuremath{\Delta}\ensuremathξ=W/\ensuremathΔ, where WWW denotes the bandwidth and \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ denotes the energy gap. For systems with LC\ensuremath≫\ensuremathξ{L}_{C}\ensuremath{\gg}\ensuremath{\xi}LC​\ensuremath≫\ensuremathξ, the threshold is governed by the electric field Vth/LC{V}_{\mathrm{th}}/{L}_{C}Vth​/LC​, which is consistent with a Landau-Zener--type breakdown Vth/LC\ensuremath∝\ensuremathΔ2/W{V}_{\mathrm{th}}/{L}_{C}\ensuremath{\propto}{\ensuremath{\Delta}}^{2}/WVth​/LC​\ensuremath∝\ensuremathΔ2/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 Vth \ensuremathΔ{V}_{\mathrm{th}}~\ensuremath{\Delta}Vth​ \ensuremathΔ regardless of the length LC{L}_{C}LC​.
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 perform density matrix renormalization group (DMRG) calculations extensively on one dimensional Mott and Peierls chains with explicit inclusion of the static bias to study the insulator-metal transition in those systems. We find that the electric field induces a number of insulator-metal transitions for finite size systems and at the thermodynamic limit, the insulating system breaks down into a completely conducting state at a critical value of bias which depends strongly on the insulating parameters. Our results indicate that the breakdown, in both the Peierls and Mott insulators, at thermodynamic limit, does not follow the Landau-Zener mechanism. Calculations on various size systems indicate that an increase in the system size decreases the threshold bias as well as the charge gap at that bias, making the insulator-metal transition sharper in both cases.
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.
We perform density matrix renormalization group (DMRG) calculations extensively on one-dimensional Mott and Peierls chains with explicit inclusion of the static bias to study the insulator–metal transition in those systems. We find that the electric field induces a number of insulator–metal transitions for finite-size systems and, at the thermodynamic limit, the insulating system breaks down into a completely conducting state at a critical value of bias that depends strongly on the insulating parameters. Our results indicate that the breakdown, in both the Peierls and Mott insulators, at the thermodynamic limit, does not follow the Landau–Zener mechanism. Calculations on various size systems indicate that an increase in the system size decreases the threshold bias as well as the charge gap at that bias, making the insulator–metal transition sharper in both cases.
Nonequilibrium transport in the one dimensional Hubbard model at half-filling is studied by the time-dependent density matrix renormalization group method. It is clearly demonstrated that dielectric breakdown of the Mott insulating phase to a nonequilibrium steady state occurs when an external voltage is larger than the charge gap. From the numerically obtained current-voltage characteristics we find that the current is suppressed by the correlation effect when compared with that of a band insulator and that the current is scaled only by the charge gap for small voltages compared to the band width.
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.