Gigantic optical nonlinearity in one-dimensional Mott–Hubbard insulators

Kishida, Hideo; Matsuzaki, Hiroyuki; Okamoto, Hiroshi; Manabe, T.; Yamashita, Masahiro; Taguchi, Y.; Tokura, Y.

doi:10.1038/35016036

Cited by 361 publications

(312 citation statements)

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“…Nonlinear optical responses: In the context of correlated electron systems, a giant nonlinearity in the optical response has been reported in 1D Mott insulators (Kishida et al, 2000;Mizuno et al, 2000).…”

Section: Overview Of Field-induced Phenomenamentioning

confidence: 99%

Nonequilibrium dynamical mean-field theory and its applications

et al. 2014

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The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultrafast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultracold atoms in optical lattices provide a new way to control and measure the time evolution of interacting lattice systems with a vastly different characteristic time scale compared to electron systems. A theoretical description of these phenomena is challenging because, first, the quantum-mechanical time evolution of many-body systems out of equilibrium must be computed and second, strong-correlation effects which can be of a nonperturbative nature must be addressed. This review discusses the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a selfconsistent impurity problem, which becomes exact in infinite dimensions. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. Insights gained into the properties of the infinite-dimensional Hubbard model under strong nonequilibrium conditions are summarized. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photodoping, and collapse-and-revival oscillations in quenched systems. Furthermore, remarkable novel phenomena have been predicted by the nonequilibrium DMFT simulations of correlated lattice systems, including dynamical phase transitions and field-induced repulsion-to-attraction conversions.

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Section: Overview Of Field-induced Phenomenamentioning

confidence: 99%

Nonequilibrium dynamical mean-field theory and its applications

et al. 2014

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“…In addition, the one dimensionality of this material enriches its physics attracting many researchers with interesting phenomena such as the spin-charge separation, a large optical nonlinear effect, and Wannier-like bound excitons. 6,7,8,9 All these factors make the excitation spectra of this system of great interest.A. S. Moskvin et al investigated the electronic structure of Sr 2 CuO 3 along and perpendicular to the chain direction by electron energy loss spectroscopy (EELS).…”

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Optical excitations inSr2CuO3

Kim

2009

Phys. Rev. B

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We investigated excitation spectra of the one-dimensional chain compound Sr2CuO3. The small peak at 2.3 eV in the loss function turned out to correspond to the strong charge transfer transition at 1.8 eV in conductivity. It has the excitonic character expected in one dimensional extended Hubbard model of the transition from the lower Hubbard band to the Zhang-Rice singlet state. The strongest peak at 2.7 eV in the loss function is attributed to the continuum excitation of the excitonic charge transfer transition. The spectral weight sum rule is satisfied within these transitions.PACS numbers: 71.27.+a, 71.35.-y, 78.20.-e, 78.67.-n Superconducting cuprates have a CuO 2 plane in common which is composed of a two dimensional (2D) cornersharing network of CuO 4 plaquettes. The electronic property of an undoped CuO 2 plane should be metallic without strong onsite Coulomb repulsion at Cu sites, which divides the Cu d x 2 −y 2 state into two Hubbard bands of upper Hubbard band (UHB) and lower Hubbard band (LHB) opening a charge transfer gap between LHB (from a hole point of a view) and O 2p states. Charge doping changes the electronic structure of the CuO 2 plane finally giving rise to the high temperature superconductivity. It is important to understand the properties of insulating cuprates to solve the mystery of the high temperature superconductivity.Optical spectroscopy is one of fundamental tools to investigate electronic structure, which can directly measure the charge transfer gap. By absorbing light, holes in LHB can be excited to O 2p states. When a hole is introduced into the CuO 2 plane, the ground state becomes a well known Zhang-Rice singlet (ZRS) state evenly residing at surrounding O 2p orbitals. 1 Because an optical excitation is a charge conserving process, to be involved in optical excitations for the ZRS state, one CuO 4 plaquette should give a hole to a neighboring CuO 4 plaquette, which is possible in corner-sharing CuO 4 plaquette structures. Therefore, the first optical excitation crossing the charge transfer gap should be from LHB to the ZRS state in the CuO 2 plane as depicted in fig. 1. The second excitation is expected to be from LHB to nonbonding (NB) O 2p states in the CuO 2 plane, which is localized within one plaquette. Energies of these two excitations are essential to model the electronic structure of the CuO 2 plane.However, the electronic structure of insulating cuprates remains still unclear. Optical spectra of insulating cuprates of 1D and 2D corner-sharing structure show similar spectral feature of two peaks around 2 eV like the peaks A and B in fig. 2. It is clear that the lowest energy peak, which is rather sharp and has a large spectral weight in common, should be the charge transfer transition α from LHB to ZRS. But the origin of the other peak, which comes at about 0.5 eV higher, is still unclear. This peak is relatively broad and the strength varies depending on materials. It is rather small and appear as a hump-like shape in RE 2 CuO 4 (RE: rare earth ions) and Sr 2 CuO 3...

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“…Fd, 71.10.Hf, 71.10.Pm, 71.30.+h The properties of quasi-one-dimensional materials have been extensively studied in recent years [1,2,3]. These materials exhibit rich phase diagrams and display unusual optical properties due to the combination of reduced dimensionality and strong electronic correlations.…”

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Ground-State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model

Jeckelmann

2002

Phys. Rev. Lett.

119

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The density-matrix renormalization group is used to study the phase diagram of the onedimensional half-filled Hubbard model with on-site (U ) and nearest-neighbor (V ) repulsion, and hopping t. A critical line Vc(U ) ≈ U/2 separates a Mott insulating phase from a charge-densitywave phase. The formation of bound charge excitations for V > 2t changes the phase transition from continuous to first order at a tricritical point Ut ≈ 3.7t, Vt = 2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line Vc(U ) for Ut < U < ∼ 7t.PACS numbers: 71.10. Fd, 71.10.Hf, 71.10.Pm, 71.30.+h The properties of quasi-one-dimensional materials have been extensively studied in recent years [1,2,3]. These materials exhibit rich phase diagrams and display unusual optical properties due to the combination of reduced dimensionality and strong electronic correlations. Consequently, much effort has been devoted to understanding the ground-state and optical properties of theoretical one-dimensional correlated electron systems such as the half-filled Hubbard model with on-site (U ) and nearest-neighbor (V ) repulsion and hopping term t. Nevertheless, the ground state phase diagram of this model is still controversial [4,5,6,7,8,9,10]. It is known [4] that the system is a Mott insulator for U > ∼ 2V and a charge density wave (CDW) insulator for U < ∼ 2V . The quantum phase transition is continuous at weak coupling (U, V ≪ t) and first order at strong coupling (U, V ≫ t). Numerically [4,5,10], one finds that the order of the transition changes at a tricritical point (U t , V t ) with V t /t ≈ 1.5 − 2.5, but this feature is not well understood. Recently, it has been proposed [8, 9, 10] that a bond-order-wave (BOW) phase exists between the Mott and CDW phases up to the tricritical point. Concurrently, the optical properties of this model have been determined in the Mott insulating phase [11,12,13,14,15]. In particular, it has been found that the lowest optical excitations consist of a pair of independent charge excitations for V ≤ 2t, while they are bound states for V > 2t. Surprisingly, the remarkable proximity of the tricritical point to the boundary between bound and free charge excitations has not been noticed until now.Here I investigate the ground-state phase diagram of the half-filled one-dimensional extended Hubbard model in the repulsive regime using the density-matrix renormalization group (DMRG) [16]. I show that the nature of the low-lying charge excitations determines the order of the transition and the position of the tricritical point. A BOW phase is found only at intermediate coupling on the critical line V c (U ) between Mott and CDW phases.The model is defined by the HamiltonianHereĉ + l,σ ,ĉ l,σ are creation and annihilation operators for electrons with spin σ =↑, ↓ at site l = 1, . . . , N,n l,σ = c + l,σĉ l,σ , andn l =n l,↑ +n l,↓ . I exclusively consider systems with an even number N of sites. At half filling the number of electrons equals N . The interaction is repul...

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Gigantic optical nonlinearity in one-dimensional Mott–Hubbard insulators

Cited by 361 publications

References 24 publications

Nonequilibrium dynamical mean-field theory and its applications

Nonequilibrium dynamical mean-field theory and its applications

Optical excitations inSr2CuO3

Ground-State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model

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