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Physical Review Letters

Anomalous transfer of spectral weight in doped strongly correlated systems

Henk J. Eskes, M.B.J. Meinders, G. A. Sawatzky

Published Aug 19, 1991• 314 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.67.1035

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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.
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 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.
Numerical results for the density of states to remove or add electrons to a finite Hubbard cluster are presented for both positive and negative on-site interactions. The behavior of the filling versus the chemical potential is discussed. At half filling there is a gap in the density of states. When the repulsive-U Hubbard model is doped spectral weight is transferred into the gap, and the chemical potential is found to move across the gap as one goes from electron to hole doping. We discuss the relationship of these results to experiment. For the negative-U Hubbard model, the chemical potential shifts continuously and lies in the middle of the superconducting gap.
In this paper we study the spectral-weight transfer from the high- to the low-energy scale by means of exact diagonalization of finite clusters for the Mott-Hubbard and charge-transfer model. We find that the spectral-weight transfer is very sensitive to the hybridization strength as well as to the amount of doping. This implies that the effective number of low-energy degrees of freedom is a function of the hybridization and therefore of the volume and temperature. In this sense it is not possible to define a Hamiltonian which describes the low-energy-scale physics unless one accepts an effective nonparticle conservation.
A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wave function for two electrons occupying the same Wannier orbital is different from the product of single-electron wave functions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as a function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transferred from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more ``dressed'' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single-hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to ``undress,'' hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.
The effect of doping in the two-dimensional Hubbard model is studied within finite temperature exact diagonalization combined with cluster dynamical mean field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto 2x2 clusters, a considerably more accurate description of the low frequency properties of the self-energy is achieved than in a pure site picture. The transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest neighbor hopping, and temperature. In particular, the self-energy component Sigma_X associated with X=(pi,0) is shown to exhibit an onset of non-Fermi-liquid behavior as the hole doping decreases below a critical value delta_c. The imaginary part of Sigma_X(omega) then develops a collective mode above E_F, which exhibits a distinct dispersion with doping. Accordingly, the real part of Sigma_X(omega) has a positive slope above E_F, giving rise to an increasing particle-hole asymmetry as the system approaches the Mott transition. This behavior is consistent with the removal of spectral weight from electron states close to E_F and the opening of a pseudogap which increases with decreasing doping. The phase diagram reveals that delta_c = 0.15 ... 0.20 for various system parameters. For electron doping, the collective mode of Sigma_X(omega) and the concomitant pseudogap are located below the Fermi energy which is consistent the removal of spectral weight from hole states just below E_F. The critical doping which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.