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arXiv:2108.12525 · Physical review. B./Physical review. B

Conducting state in a Mott insulator induced by a staggered field

X. Z. Zhang, Z. Song

Published Feb 1, 2022• 1 citation
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Abstract

Quenching has recently emerged as a transformative tool for dynamically evolving quantum systems into nonequilibrium phases with desirable properties. In the context of strongly correlated systems, such a tool can significantly alter their microscopic behavior and manifest a variety of interesting phenomena at the macroscopic level. We show that the staggered magnetic field can induce a nonequilibrium steady conducting state from the deep Mott insulating phase. The underlying mechanism can be abstracted from two-particle subspace, that is, the resonant staggered field combined with on-site interaction forced the particles to pair up and move like a free single particle. Correspondingly, the bound pair can have large energy bandwidth and exhibits the following dynamical behaviors. (i) When an electric field is applied, fast bound pair Bloch oscillation occurs, while a single electron is frozen. (ii) When a quenching resonant field is applied to an initial antiferromagnetic Mott insulating state, the final state becomes a doublon conducting state manifested by the nonzero $\ensuremath{\eta}$ correlator and large charge fluctuation. Our findings indicate that the cooperation of electron-electron correlation and modulated external field can provide an alternative pathway to access a new exotic quantum state that is absent in the ground-state phase diagram.

DOI
10.1103/physrevb.105.054302

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Quenching has recently emerged as a transformative tool for dynamically evolving quantum systems into nonequilibrium phases with desirable properties. In the context of strongly correlated systems, such a tool can significantly alter their microscopic behavior and manifest a variety of interesting phenomena at the macroscopic level. We show that the staggered magnetic field can induce a nonequilibrium steady conducting state from the deep Mott insulating phase. The underlying mechanism can be abstracted from two-particle subspace, that is, the resonant staggered field combined with on-site interaction forced the particles to pair up and move like a free single particle. Correspondingly, the bound pair can have large energy bandwidth and exhibits the following dynamical behaviors. (i) When an electric field is applied, fast bound pair Bloch oscillation occurs, while a single electron is frozen. (ii) When a quenching resonant field is applied to an initial antiferromagnetic Mott insulating state, the final state becomes a doublon conducting state manifested by the nonzero \ensuremathη\ensuremath{\eta}\ensuremathη correlator and large charge fluctuation. Our findings indicate that the cooperation of electron-electron correlation and modulated external field can provide an alternative pathway to access a new exotic quantum state that is absent in the ground-state phase diagram.
A many-body quantum system with varying parameters can exhibit two distinct quantum states within the same energy shell. This allows for a dynamic transition from the ground state of the pre-quench Hamiltonian to a steady state of the post-quench Hamiltonian. We investigate the dynamic response of the ground states in a two-layer half-filled Hubbard model to a perpendicular electric field. We demonstrate that the steady state exhibits conductivity when the field is in resonance with the on-site repulsion, while the initial state is a Mott-insulating state. Additionally, the two layers exhibit identical conducting behavior due to the formation of long-lived dopings, as evidenced by the charge fluctuation. The key factor in achieving this dynamic transition is the cooperative interplay between on-site interactions and the resonant field, rather than the individual roles they play. Our findings offer an alternative mechanism for field-induced conductivity in strongly correlated systems.
We show that a resonant pulsed field can induce a steady superconducting state even in the deep Mott insulating phase of the dimerized Hubbard model. The superconductivity found here in the nonequilibrium steady state is due to the $\ensuremath{\eta}$-pairing mechanism, characterized by the existence of the off-diagonal long-range order (ODLRO), and is absent in the ground-state phase diagram. The key of the scheme lies in the generation of the field-induced charge density wave (CDW) state that is from the valence bond solid. The dynamics of this state resides in the highly excited subspace of the dimerized Hubbard model and is dominated by a $\ensuremath{\eta}$-spin ferromagnetic model. The decay of such long-living excitation is suppressed because of energy conservation. We also develop a dynamical method to detect the ODLRO of the nonequilibrium steady state. Our finding demonstrates that the nonequilibrium many-body dynamics induced by the interplay between the resonant external field and electron-electron interaction is an alternative pathway to access a new exotic quantum state, and also provides an alternative mechanism for enhancing superconductivity.
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.
The study of nonequilibrium phenomena in interacting lattice systems can provide new perspectives on correlation effects, and information on metastable states of matter. Mott insulators are a promising class of systems for nonequilibrium studies, since they exhibit exotic phenomena and complex phase diagrams upon doping, and because a large Mott gap provides protection against fast thermalization and heating after photo-excitations. We can thus expect the emergence of interesting transient states and photo-induced phases in Mott systems. This review presents the current understanding of the mechanisms which control the time evolution of photo-doped charge carriers and the properties of photo-induced metastable states. We focus on recent theoretical progress, identify the relevant underlying concepts, and link them to experimental observations. The review starts with a general discussion of field-induced nonequilibrium setups and an overview of key experiments which revealed characteristic properties of photo-excited Mott states, proceeds with a compact overview of the theoretical tools which have been developed to investigate these strongly correlated nonequilibrium states, and then analyzes Mott insulators driven out of equilibrium by static electric fields, periodic fields, and short laser pulses. We also discuss the appearance of nonthermal electronic orders in photo-excited Mott systems, including nonthermal spin and orbital orders, ηηη pairing states, and novel types of excitonic orders.
Correlated systems are a wide class of materials in which the strong electron-electron repulsion is the origin of very fascinating and unusual properties, among which metal-to-insulator transitions and high temperature superconductivity are the most striking examples. In the recent years, the fast development of non-adiabatic probing techniques opened new interesting perspectives for the investigation of such materials in non-equilibrium conditions. In this thesis, we discuss the theoretical description of few relevant cases which represent different examples of non-equilibrium phenomena in correlated materials. In particular, we will focus on the dynamics following a sudden excitation and the coupling to an external driving field. As a first example we consider the dynamics across a phase transition, namely we explore the possibility of driving a phase transition as the result of a sudden excitation, as e.g. the coupling with a short light pulse. We consider systems showing different equilibrium phases and study the conditions under which the off-equilibrium dynamics may lead to non-trivial dynamical phase transitions. A different case is represented by the dynamics induced by a driving electric field. This problem is particularly relevant for the possible applications of correlated materials in electronic devices. Here we consider the paradigmatic case of a correlated material coupled to external sources which impose a finite bias across the system. We analyze the formation and the properties of the non-equilibrium stationary states in which a finite current flows through the system. This allows us to study the non-linear response properties of a correlated system. In this context, a particularly relevant aspect is the problem of the dielectric breakdown of a Mott insulator, namely the formation of conducting states in the Mott insulating phase. In this thesis we explore different mechanisms leading to such possibility. First we discuss a quantum tunneling mechanism of carriers driven across the insulating gap by the effect of strong electric-fields. Eventually, we discuss the possibility of a resistive transition from an insulating to a metallic state induced by the application of an external electric-field.
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.