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arXiv:1106.0604 · Physical Review Letters

Integrable Mott Insulators Driven by a Finite Electric Field

Marcin Mierzejewski, J. Bonča, Peter Prelovšek

Published Sep 14, 2011• 38 citations
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Abstract

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.

DOI
10.1103/physrevlett.107.126601

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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.
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 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.
Nonlinear real-time response of interacting particles is studied on the example of a one-dimensional tight-binding model of spinless fermions driven by electric field. Using equations of motion and numerical methods we show that for a nonintegrable case at finite temperatures the major effect of nonlinearity can be taken into account within the linear response formalism extended by a renormalization of the kinetic energy due to the Joule heating. On the other hand, integrable systems show on constant driving a different universality with a damped oscillating current whereby the frequency is related but not equal to the Bloch oscillations.
We study numerically how conservation laws affect the optical conductivity σ(ω) of a slightly doped one-dimensional Mott insulator. We investigate a regime where the average distance between charge excitations is large compared to their thermal de Broglie wavelength and a classical description is possible. Due to conservation laws, the dc conductivity is infinite and the Drude weight D is finite even at finite temperatures. Our numerical results test and confirm exact theoretical predictions for D both for integrable and non-integrable models. Small deviations from integrability induce slowly decaying modes and, consequently, low-frequency peaks in σ(ω), which can be described by a memory matrix approach.
We characterize the response of a Mott insulating system to a static electric field in terms of its conducting and spectral properties. Dissipation is included by a coupling to fermionic baths and to either optical or acoustic phonons. This paper extends and completes the analysis made in a previous work by the authors [Mazzocchi et al., Phys. Rev. B 106, 125123 (2022)]. In the present work, phonons are included diagrammatically within the Migdal approximation by also including self-consistency from the electronic feedback. The nonequilibrium steady state is addressed by means of the dynamical mean-field theory based on the nonequilibrium Green's function approach, while the so-called auxiliary master equation approach is employed as impurity solver. With optical phonons the self-consistency suppresses the steady-state current for field strengths comparable to the band gap with respect to the non-self-consistent case. This is due to the interaction of phonons with the hot electrons of the lattice which increases their temperature, thus providing a less effective relaxation channel for the current-induced Joule heat. In addition, in the case of optical phonons, the results are essentially independent of the temperature of the fermionic baths, as the latter is sensibly smaller than their characteristic frequency. On the other hand, with acoustic phonons the steady-state current is slightly suppressed by the self-consistent treatment only at field strengths close to half of the gap and especially at very small phonon frequency. Also, in this case, the results seem to slightly depend on the temperature of the fermionic baths.