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arXiv:cond-mat/9704004 · Europhysics Letters (EPL)

Charged excitons in doped extended Hubbard model systems

Jeroen van den Brink, R. Eder, G. A. Sawatzky

Published Mar 1, 1997• 15 citations
arXivHTMLPDF

Abstract

We show that the charge transfer excitons in a Hubbard model system including nearest-neighbor Coulomb interactions effectively attain some charge in doped systems and become visible in photoelectron and inverse photoelectron spectroscopies. This shows that the description of a doped system by an extended Hubbard model differs substantially from that of a simple Hubbard model. Longer-range Coulomb interactions cause satellites in the one-electron removal and addition spectra and the appearance of spectral weight in the gap of doped systems at energies corresponding to the excitons of the undoped systems. The spectral weight of the satellites is proportional to the doping times the coordination number and therefore is strongly dependent on the dimension.

DOI
10.1209/epl/i1997-00174-3

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Physical review. B, Condensed matter•Oct 1, 1996•5 citations
We show that the charge transfer excitons in a Hubbard model system including nearest-neighbor Coulomb interactions effectively attain some charge in doped systems and become visible in photoelectron and inverse photoelectron spectroscopies. This shows that the description of a doped system by an extended Hubbard model differs substantially from that of a simple Hubbard model. Longer-range Coulomb interactions cause satellites in the one-electron removal and addition spectra and the appearance of spectral weight in the gap of doped systems at energies corresponding to the excitons of the undoped systems. The spectral weight of the satellites is proportional to the doping times the coordination number and therefore is strongly dependent on the dimension.
We present a theoretical description of the one-particle excitation spectra in strongly correlated systems with nonlocal interactions. Using exact diagonalization techniques, photoemission and inverse photoemission spectra of an extended Hubbard model with an intersite Coulomb interaction are calculated. The single-particle and many-body aspects are treated on an equal footing. The hopping and interaction parameters are adjusted to simulate various Hubbard and charge-transfer systems. In contrast to normal expectations, the intersite interaction is found to suppress the spectral features driven by the on-site interaction, leading to a narrowing in the overall spectral distribution. It also produces qualitatively new behavior in the spin polarization of the spectra and in the doping dependence of the low-energy spectral weight. The degree of sensitivity of the spectra to the single-particle and interaction parameters is systematically investigated. General implications of the calculated results for strongly correlated systems are discussed.
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.
We show that charge excitations within one-dimensional extended Hubbard models in the limit of large on-site Coulomb interaction can be mapped onto pairs of spin reversals from the ferromagnetic Ising-Heisenberg spin Hamiltonian. The exciton in the extended Hubbard models is equivalent to the bound two-magnon state of the spin Hamiltonian. From exact results for the spin Hamiltonian, for the intersite Coulomb interactions limited between nearest neighbors, the lowest optical exciton is separated in energy from the electron-hole continuum only for the intersite interaction larger than half the one-electron bandwidth. The commutation relationship between spin operators allows us to numerically investigate exciton binding energies and optical absorptions from the ground state in the limit of large on-site Coulomb interaction even for cases where analytic results are not available. For intersite Coulomb interaction limited between nearest neighbors, the binding energy of the lowest optical exciton changes very weakly for realistic Peierls bond dimerization, although there is a profound change in the optical absorption. While in the undimerized chain a single optical exciton can occur, two additional excitons that occur above the threshold of the electron-hole continuum become optically visible in the dimerized case. For long-range intersite Coulomb interactions, multiple excitons can occur even for the undimerized chain, and additional exciton states become optically visible upon dimerization. With the 1/r1/r1/r form for the intersite Coulomb interaction, our numerical calculations suggest that the formation of at least one optical exciton is unconditional, unlike the case of nearest-neighbor interaction. The binding energy of the lowest optical exciton again depends weakly on the dimerization for long-range interaction. Our theoretical results can explain the occurrence of two charge-transfer absorption bands in half-filled band segregated stack charge transfer solids below the spin-Peierls dimerization temperature. Our results also suggest that the lowest optical state of \ensuremath{\pi}-conjugated polymers, in which Coulomb interactions are long ranged, is necessarily an exciton.
Electronic correlations arise from the competition between the electrons' kinetic and Coulomb interaction energy and give rise to a rich phase diagram and many emergent quasiparticles. The binding of doubly-occupied and empty sites into a doublon-holon exciton is an example of this in the Hubbard model. Unlike traditional excitons in semiconductors, in the Hubbard model it is the kinetic energy which provides the binding energy. Upon doping, we find the emergence of exciton complexes, such as a holon-doublon-holon trion. The appearance of these low-lying collective excitations make screening more effective in the doped system. As a result, Hubbard-based modelling of correlated materials should use different values of UUU for the doped system and the insulating parent compound, which we illustrate using the cuprates as an example.
Calculations of the single-particle spectral function for the two-band Hubbard model as a function of doping and nearest-neighbor Coulomb repulsion are performed on finite-size clusters. It is shown that for hole doping the effect of the nearest-neighbor Coulomb repulsion leads to the effective pinning of the Fermi energy, and to the creation of new states in the charge-transfer gap. For electron doping, however, the model behaves as a one-band Hubbard model with the Fermi energy moving into the conduction band. The results of this calculation are in qualitative agreement with some of the spectroscopic studies of the electronic structure at the Fermi energy of the high-temperature cuprate superconductors.
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.