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Journal of Physics Conference Series

Photo-induced metallic liquid in a one-dimensional Mott insulator in AC fields

Takashi Oka, Hideo Aoki

Published Mar 1, 2009• 0 citations
Publisher

Abstract

We theoretically study the properties of the photo-carriers created in a one-dimensional Mott insulator subject to strong AC electric fields. The time-dependent density matrix renormalization group method is used to calculate the nonlinear optical conductivity, for which a metallic, gapless mode is found to emerge. The mode has linear dispersion with a charge velocity that differs from the free electron velocity, which indicates that the photo-doped carriers behave collectively as in the Tomonaga-Luttinger liquid.

DOI
10.1088/1742-6596/150/4/042152

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We theoretically study the properties of the photo-carriers created in a one-dimensional Mott insulator subject to strong AC electric fields. The time-dependent density matrix renormalization group method is used to calculate the nonlinear optical conductivity, for which a metallic, gapless mode is found to emerge. The mode has linear dispersion with a charge velocity that differs from the free electron velocity, which indicates that the photo-doped carriers behave collectively as in the Tomonaga-Luttinger liquid.
Photoinduced metallic states in a Mott insulator are studied for the half-filled one-dimensional Hubbard model with the time-dependent density-matrix renormalization group. An irradiation of strong ac fields is found to create, in the nonequilibrium steady state, a linear dispersion in the optical spectrum (current-current correlation) reminiscent of the Tomonaga-Luttinger liquid for the doped Mott insulator in equilibrium. The spin spectrum in nonequilibrium retains the des Cloizeaux--Pearson mode with the spin velocity differing from the charge velocity. The mechanism of the photocarrier doping, along with the renormalization in the charge velocity, is analyzed in terms of an effective Dirac model.
The density-matrix renormalization-group (DMRG) method is used to investigate optical excitations in the Mott insulating phase of a one-dimensional extended Hubbard model. The linear optical conductivity is calculated using the dynamical DMRG method and the nature of the lowest optically excited states is investigated using a symmetrized DMRG approach. The numerical calculations agree perfectly with field-theoretical predictions for a small Mott gap and analytical results for a large Mott gap obtained with a strong-coupling analysis. It is shown that four types of optical excitations exist in this Mott insulator: pairs of unbound charge excitations, excitons, excitonic strings, and charge-density-wave (CDW) droplets. Each type of excitation dominates the low-energy optical spectrum in some region of the interaction parameter space and corresponds to distinct spectral features: a continuum starting at the Mott gap (unbound charge excitations), a single peak or several isolated peaks below the Mott gap (excitons and excitonic strings, respectively), and a continuum below the Mott gap (CDW droplets).
We consider the two-terminal conductance of a one-dimensional Mott insulator undergoing the commensurate-incommensurate quantum phase transition to a conducting state. We treat the leads as Luttinger liquids. At a specific value of compressibility of the leads, corresponding to the Luther-Emery point, the conductance can be described in terms of the free propagation of noninteracting fermions with charge e∕2e∕\sqrt{2}e∕2​. At that point, the temperature dependence of the conductance across the quantum phase transition is described by a Fermi function. The deviation from the Luther-Emery point in the leads changes the temperature dependence qualitatively. In the metallic state, the low-temperature conductance is determined by the properties of the leads, and is described by the conventional Luttinger-liquid theory. In the insulating state, conductance occurs via activation of e∕2e∕\sqrt{2}e∕2​ charges, and is independent of the Luttinger-liquid compressibility.
We study the interplay between an on-site Hubbard repulsion and quasiperiodic potential in one-dimensional fermion chains using the density matrix renormalization group. We find that, at half filling, the quasiperiodic potential can destroy the Mott gap, leading to a metallic Luttinger liquid phase between the gapped Mott insulator at strong repulsion and the localized gapless Aubry-Andr\'e insulator at strong quasiperiodic potential. Away from half filling, the metallic phase of the interacting model persists to larger critical strengths of the potential than in the noninteracting case, suggesting interaction-stabilized delocalization at finite doping. We characterize the Luttinger liquid through its charge and spin correlations, structure factors, and entanglement entropy.
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.