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Journal of the Physical Society of Japan

Carrier Concentration Dependence of Spectral Functions in Strongly Correlated System – Study by the Dynamical Mean Field Theory –

Tetsuya Mutou, Hideaki Takahashi, Dai S. Hirashima

Published Sep 15, 1997• 8 citations
Publisher

Abstract

We study the formation of itinerant electronic states on carrier doping in a strongly correlated insulator by calculating one-particle-excitation spectral functions. We apply (1) the quantum Monte Carlo method and (2) the exact diagonalization method in the framework of the dynamical mean field theory to a two-band Hubbard model. The parameters of the model are chosen so that the undoped system is a charge-transfer-type insulator. We find that the itinerant states originate from local singlet states formed by hybridized d - and p -holes. We also find asymmetry between hole-doped and electron-doped cases: (1) in the electron-doped case a peak is not observed at the chemical potential in contrast to the hole-doped case; and (2) the mass-enhancement factor in the electron-doped case is smaller than that in the hole-doped case. The results of the one-particle-excitation spectrum and the mass-enhancement factor are discussed in the light of experimental and theoretical results for high- T c cuprates.

DOI
10.1143/jpsj.66.2781

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We study the formation of itinerant electronic states on carrier doping in a strongly correlated insulator by calculating one-particle-excitation spectral functions. We apply (1) the quantum Monte Carlo method and (2) the exact diagonalization method in the framework of the dynamical mean field theory to a two-band Hubbard model. The parameters of the model are chosen so that the undoped system is a charge-transfer-type insulator. We find that the itinerant states originate from local singlet states formed by hybridized d - and p -holes. We also find asymmetry between hole-doped and electron-doped cases: (1) in the electron-doped case a peak is not observed at the chemical potential in contrast to the hole-doped case; and (2) the mass-enhancement factor in the electron-doped case is smaller than that in the hole-doped case. The results of the one-particle-excitation spectrum and the mass-enhancement factor are discussed in the light of experimental and theoretical results for high- T c cuprates.
We study the spectral weight transfer and the chemical potential shift in strongly correlated electron systems caused by carrier doping by applying the dynamical mean-field theory to a two-band Hubbard model. The parameters of the model are chosen so that the undoped system is a charge-transfer-type insulator. We find that in the insulating phase there are finite intensities corresponding to local singlet states formed by hybridized d and p electrons, and that, on doping a part of them, turn into itinerant states. The results are discussed in the light of experimental and theoretical results for high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates. \textcopyright{} 1996 The American Physical Society.
We systematically examine the asymmetry of the electronic states in the hole- and electron-doped cuprates by using a $t\text{\ensuremath{-}}J$ model with the second-neighbor hopping ${t}^{\ensuremath{'}}$ and third one ${t}^{\ensuremath{''}}$ (the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model). Numerically exact diagonalization method is employed for a 20-site square lattice. We impose twisted boundary conditions (BC) instead of standard periodic BC. For static and dynamical correlation functions, averaging procedure over the twisted BC is used to reduce the finite-size effect. We find that antiferromagnetic spin correlation remains strong in electron doping in contrast to the case of hole doping, being similar to the case of the periodic BC. This leads to a remarkable electron-hole asymmetry in the dynamical spin structure factor and two-magnon Raman scattering. By changing the twist, the single-particle spectral function is obtained for all momenta in the Brillouin zone. Examining the spectral function in detail, we find a gap opening at around the $\mathbf{k}=(\ensuremath{\pi},0)$ region for 10% doping of holes (the carrier concentration x=0.1x=0.1x=0.1), leading to a Fermi arc that is consistent with experiments. In electron doping, however, a gap opens at around $\mathbf{k}=(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ and persists up to x=0.2x=0.2x=0.2, being correlated with the strength of the antiferromagnetic correlation. We find that the magnitude of the gaps is sensitive to ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$. A pseudogap is also seen in the optical conductivity for electron doping, and its magnitude is found to be the same as that in the spectral function. We compare calculated quantities with corresponding experimental data, and discuss similarities and differences between them as well as their implications.
The spectral weight functions and the optical conductivity of a highly correlated electronic system described by a simple Hubbard model are studied. The calculations are carried out for a small system, a cubic cluster of eight sites, by means of exact diagonalization using symmetrized basis functions. The spectral weight functions of a single hole (or electron) placed in an otherwise half-filled band are obtained. The density of states at different interaction strengths, ranging from weak to strong couplings, is studied. We observe the spreading of the spectral weight associated with some single-particle eigenstates over a large range of energies, and the appearance of satellite structure at higher excitation energies. The nature of band narrowing is also discussed. The frequency dependent (optical) conductivity is studied for the cases of a half-filled band, and for one hole and two hole dopings away from half filling. The interaction strength is varied between the weak- and strong-coupling limits. The formation of a Hubbard gap is observed. Results are related to aspects of the metal-insulator transition in bulk systems.
We study theoretically the simultaneous photoinduced two-particle excitations of strongly correlated systems on the basis of the Hubbard model. Under certain conditions specified in this work, the corresponding transition probability is related to the two-particle spectral function which we calculate using three different methods: the dynamical mean-field theory combined with quantum Monte Carlo technique, the first-order perturbation theory and the ladder approximations. The results are analyzed and compared for systems at the verge of the metal-insulator transitions. The dependencies on the electronic correlation strength and on doping are explored. In addition, the account for the orbital degeneracy allows an insight into the influence of interband correlations on the two-particle excitations. A suitable experimental realization is discussed.
In the generalized-tJtJtJ model the effect of a large local Coulomb repulsion is accounted for by restricting the Hilbert space to states with at most one electron per site. In this case the electronic system can be viewed in terms of holes hopping in a lattice of correlated spins, where holes are the carriers doped into the half-filled Mott insulator. To explicitly capture the interplay between the hole dynamics and local spin correlations we derive a formulation of the generalized-tJtJtJ model where doped carrier operators are used instead of the original electron operators. This ``doped carrier'' formulation provides a starting point to address doped spin systems, and we use it to develop a fully fermionic, mean-field description of doped Mott insulators. This mean-field approach reveals a mechanism for superconductivity---namely, spinon-dopon mixing---and we apply it to the $t{t}^{\ensuremath{'}}{t}^{\ensuremath{''}}J$ model as of interest to high-temperature superconductors. In particular, we use model parameters borrowed from band calculations and from fitting angle-resolved photoemission spectroscopy data to obtain a mean-field phase diagram that reproduces semiquantitatively that of hole- and electron-doped cuprates. The mean-field approach hereby presented accounts for the local antiferromagnetic and ddd-wave superconducting correlations which, we show, provide a rational for the role of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ in strengthening superconductivity as expected by experiments and other theoretical approaches. As we discuss how ttt, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$ affect the phase diagram, we also comment on possible scenarios to understand the differences between as-grown and oxygen-reduced electron-doped samples.
A qualitative and quantitative description (exact diagonalization of finite clusters) of the doping dependence of one-electron-removal and -addition spectral weights is given. A half-filled Hubbard system in the localized limit has two low-energy electron-addition (removal) states for each hole (electron) created by doping. In contrast, a charge-transfer system in the localized limit is fundamentally asymmetric between hole and electron doping. However, when the hybridization is increased this asymmetry disappears quickly and both holes and electrons introduced by doping show a strongly correlated behavior.