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arXiv:1410.0626 · Physical Review Letters

Electric-Field-Driven Resistive Switching in the Dissipative Hubbard Model

Jiajun Li, Camille Aron, Gabriel Kotliar, Jong E. Han

Published Jun 4, 2015• 69 citations
arXivHTMLPDF

Abstract

We study how strongly correlated electrons on a dissipative lattice evolve out of equilibrium under a constant electric field, focusing on the extent of the linear regime and hysteretic nonlinear effects at higher fields. We access the nonequilibrium steady states, nonperturbatively in both the field and the electronic interactions, by means of a nonequilibrium dynamical mean-field theory in the Coulomb gauge. The linear response regime, limited by Joule heating, breaks down at fields much smaller than the quasiparticle energy scale. For large electronic interactions, strong but experimentally accessible electric fields can induce a resistive switching by driving the strongly correlated metal into a Mott insulator. We predict a nonmonotonic upper switching field due to an interplay of particle renormalization and the field-driven temperature. Hysteretic I-V curves suggest that the nonequilibrium current is carried through a spatially inhomogeneous metal-insulator mixed state.

DOI
10.1103/physrevlett.114.226403

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We study how strongly correlated electrons on a dissipative lattice evolve out of equilibrium under a constant electric field, focusing on the extent of the linear regime and hysteretic nonlinear effects at higher fields. We access the nonequilibrium steady states, nonperturbatively in both the field and the electronic interactions, by means of a nonequilibrium dynamical mean-field theory in the Coulomb gauge. The linear response regime, limited by Joule heating, breaks down at fields much smaller than the quasiparticle energy scale. For large electronic interactions, strong but experimentally accessible electric fields can induce a resistive switching by driving the strongly correlated metal into a Mott insulator. We predict a nonmonotonic upper switching field due to an interplay of particle renormalization and the field-driven temperature. Hysteretic I-V curves suggest that the nonequilibrium current is carried through a spatially inhomogeneous metal-insulator mixed state.
Novel physics arises when strongly correlated system is driven out of equilibrium by external fields. Dramatic changes in physical properties, such as conductivity, are empirically observed in strongly correlated materials under high electric field. In particular, electric-field driven metal-insulator transitions are well-known as the resistive switching effect in a variety of materials, such as VO2_22​, V2_22​O3_33​ and other transition metal oxides. To satisfactorily explain both the phenomenology and its underlying mechanism, it is required to model microscopically the out-of-equilibrium dissipative lattice system of interacting electrons. In this thesis, we developed a systematic method of modeling non-equilibrium steady states for dissipative lattice systems by means of Non-equilibrium Green's function and Dynamical Mean Field Theory. We firstly establish a "minimum model" to formulate the strong-field transport in non-interacting dissipative electron lattice. This model is exactly soluble and convenient for discussing energy dissipation and steady-state properties. The formalism is then combined with Dynamical Mean Field Theory to provide a systematic framework describing the nonequilibrium steady-state of correlated materials. We use the formalism to study the strong-field transport properties of correlated materials, Mott insulators and Dirac electrons in graphene. We concentrate on the microscopic description of resistive switching. Of particular interest is the filament formation during the dynamical phase transition, which has been interpreted as a result of the delicate interplay between dissipation and Mott physics. We will also examine IVIVIV characteristics and particularly the current saturation of Dirac electrons in graphene. The arXiv version has been updated with minor modifications and corrections.
In this work, we develop a non-equilibrium steady-state non-crossing approximation (NESS-NCA) impurity solver applicable to general impurity problems. The choice of the NCA as the impurity solver enables both a more accurate description of correlation effects with larger Coulomb interaction and scalability to multi-orbital systems. Based on this development, we investigate strongly correlated non-equilibrium states of a dissipative lattice system under constant electric fields. Both the electronic Coulomb interaction and the electric field are treated non-perturbatively using dynamical mean-field theory in its non-equilibrium steady-state form (NESS-DMFT) with the NESS-NCA impurity solver. We validate our implementation using a half-filled single-band Hubbard model attached to a fictitious free Fermion reservoir, which prevents temperature divergence. As a result, we identify metallic and insulating phases as functions of the electric field and the Coulomb interaction along with a phase coexistence region amid the metal-to-insulator transition (MIT). We find that the MIT driven by the electric field is qualitatively similar to the equilibrium MIT as a function of temperature, differing from results in previous studies using the iterative perturbation theory (IPT) impurity solver. Finally, we highlight the importance of the morphology of a correlated system under the influence of an electric field.
Understanding strongly correlated systems driven out of equilibrium is a challenging task necessitating the simultaneous treatment of quantum mechanics, dynamical constraints, and strong interactions. A Mott insulator subjected to a uniform and static electric field is prototypical, raising key questions such as the fate of Bloch oscillations with increasing correlation strength, the approach to a steady-state DC transport regime and the role of dissipation in it, and electric-field-driven phase transitions. Despite tremendous efforts over the past decade employing various numerical and analytical approaches, the manner in which a nonequilibrium steady state gets established has remained an unresolved problem. We develop here an effective large-N\mathcal{N}N Keldysh field theory for studying nonequilibrium transport in a regular one-dimensional dissipative Mott insulator system subjected to a uniform electric field. Upon abruptly turning on the electric field (a quench), a transient oscillatory current response reminiscent of Bloch oscillations is found. In the regime of small tunneling conductance the amplitude of these oscillations, over a large time window, decreases as an inverse square power law in time, ultimately going over to an exponential decay beyond a large characteristic time ${\ensuremath{\tau}}_{d}$ that increases with N.\mathcal{N}.N. Such a relaxation to a steady-state DC response is absent in the dissipation-free Hubbard chain at half filling. The steady-state current at small fields is governed by large-distance cotunneling, a process absent in the equilibrium counterpart. The low-field DC current has a Landau-Zener-Schwinger form but qualitatively differs from the expression for pair-production probability for the dissipation-free counterpart. The breakdown of perturbation theory in the Mott phase possibly signals a nonequilibrium phase transition to a metallic phase. Our study sheds light on the approach of a driven, dissipative strongly correlated system to a nonequilibrium steady state and also provides a general analytic microscopic framework for understanding other nonequilibrium phenomena in these systems.
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.
We study the steady-state dynamics of the Hubbard model driven out of equilibrium by a constant electric field and coupled to a dissipative heat bath. For a very strong field, we find a dimensional reduction: the system behaves as an equilibrium Hubbard model in lower dimensions. We derive steady-state equations for the dynamical mean-field theory in the presence of dissipation. We discuss how the electric field induced dimensional crossover affects the momentum resolved and integrated spectral functions, the energy distribution function, as well as the steady current in the nonlinear regime.
We develop a method for extracting the steady nonequilibrium current from studies of driven isolated systems, applying it to the model of a one-dimensional Mott insulator at high temperatures. While in the nonintegrable model the nonequilibrium conditions can be accounted for by internal heating, the integrability leads to a strongly nonlinear dc response with a vanishingly small dc conductivity in the linear-response regime. The finding is consistent with equilibrium results for the dc limit of the optical conductivity determined in the presence of a weak and decreasing perturbation.