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Bulletin of the American Physical Society

Nonequilibrium Electron Transport in Mott Insulators

K. A. Al-Hassanieh, Fabian Heidrich‐Meisner, Iván González, Elbio R. Dagotto, A. E. Feiguin, Marcelo J. Rozenberg

Published Mar 6, 2007• 0 citations
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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 establish the nonequilibrium thermal phases of a voltage driven antiferromagnetic Mott insulator in three dimensions, realized at steady state under a voltage bias. Starting from the Keldysh action for the half-filled Hubbard model, we derive an effective Langevin equation for the ``slow'' magnetic variables. The coupling of electrons to these degrees of freedom determine the transport properties. At low temperature we find a voltage-driven discontinuous insulator-metal transition, along with hysteresis. We map the suppression of the N\'eel temperature TN{T}_{N}TN​ and pseudogap temperature Tpg{T}_{\text{pg}}Tpg​ with increasing voltage, and discover that the biased Mott insulator has a finite temperature insulator-metal transition. The low temperature results resolve an experimental puzzle about hysteresis, and the thermal results make testable predictions on spectra and nonlinear transport.
We study the spectral and transport properties of a Mott insulator driven by a static electric field into a nonequilibrium steady state. For the dissipation, we consider two mechanisms: wide band fermion reservoirs and phonons included within the Migdal approximation. The electron correlations are treated via nonequilibrium dynamical mean field theory with an impurity solver suitable for strong correlations. We find that dissipation via phonons is limited to restricted ranges of field values around Wannier-Stark resonances. To cover the full range of field strengths, we allow for a small coupling with fermionic baths, which stabilizes the solution. When considering both dissipation mechanisms, we find that phonons enhance the current for field strengths close to half of the gap while lowering it at the gap resonance as compared to the purely electronic dissipation used by Murakami and Werner [Murakami and Werner, Phys. Rev. B 98, 075102 (2018)]. Once phonons are the only dissipation mechanism, the current in the metallic phase is almost one order of magnitude smaller than the typical values obtained by coupling to a fermionic bath. In this case, the transport regime is characterized by an accumulation of charge in the upper Hubbard band described by two effective chemical potentials.