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arXiv:cond-mat/9503081 · Europhysics Letters (EPL)

Charge Transfer Excitons and Possible Excitonic Pairing in the Extended Two-Band Hubbard Model

C Vermeulen, William Barford, Eduardo R. Gagliano

Published Aug 1, 1995• 3 citations
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Abstract

Exact diagonalisations of the extended two-band Hubbard model are performed. In the insulating regime it is shown that the nearest-neighbour copper-oxygen repulsion, V , leads to Frenkel excitons in the charge transfer gap at values of V of the order of copper-oxygen hybridisation, t . In the metallic regime it is shown that the static charge transfer and density-density correlation functions diverge as a function of V , indicating a charge transfer instability and phase separation. This is accompanied by a softening of the q → 0 mode of the dynamic correlation functions which is associated with the excitonic excitations responsible for the superconducting correlations observed in the proximity of the phase separation boundary described by C. Vermeulen et al. (C. Vermeulen et al. , Europhys. Lett. , 28 (1994) 653).

DOI
10.1209/0295-5075/31/4/007

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Exact diagonalisations of the extended two-band Hubbard model are performed. In the insulating regime it is shown that the nearest-neighbour copper-oxygen repulsion, V , leads to Frenkel excitons in the charge transfer gap at values of V of the order of copper-oxygen hybridisation, t . In the metallic regime it is shown that the static charge transfer and density-density correlation functions diverge as a function of V , indicating a charge transfer instability and phase separation. This is accompanied by a softening of the q → 0 mode of the dynamic correlation functions which is associated with the excitonic excitations responsible for the superconducting correlations observed in the proximity of the phase separation boundary described by C. Vermeulen et al. (C. Vermeulen et al. , Europhys. Lett. , 28 (1994) 653).
The effects of the nearest neighbour Coulomb repulsion, V, are considered in the one dimensional copper-oxide chain using the modified Lanczos method. Above a critical value of V we find that charge transfer excitons are the lowest lying energy exitations in the insulating phase. Close to the metal-insulator transition and V=0V=0V=0 there is good `particle-hole' symmetry, showing that the mapping from a two band model to a one band model is appropriate. The effect of the nearest neighbour repulsion is to create states in the gap and to pin the Fermi level upon hole doping.
We analyze the dynamics of the charge degrees of freedom in the extended Hubbard model for the CuO2{\mathrm{CuO}}_{2}CuO2​ planes in copper oxides in the strong-coupling limit. We analyze the behavior of the collective modes near the charge-transfer instability (CTI). The CTI is driven by an overdamped zero-sound mode when the Landau stability criterion F0s{\mathit{F}}_{0}^{\mathit{s}}F0s​>-1 is violated due to the charge-transfer mode-mediated attraction. The divergence of the compressibility at the CTI requires a Maxwell construction, which determines a region of phase separation. Near the phase-separation boundary, at intermediate doping, the singlet Cooper coupling is attractive both in the s- and d-wave channels. In the strong-coupling limit the excitonic energy ${\mathrm{\ensuremath{\omega}}}_{\mathrm{exc}}$ is large and the energy scale for pairing is the Fermi energy itself.
High-temperature superconductivity emerges upon doping a state of matter that is insulating because of interactions. A widely studied model considers one orbital per CuO2{\mathrm{CuO}}_{2}CuO2​ unit cell on a square lattice with a strong intraorbital repulsion that leads to a so-called Mott-Hubbard insulator. Here we solve a model that takes into account, within each unit cell, two oxygen orbitals where there is no electron-electron repulsion and a copper orbital with strong electron-electron repulsion. The insulating phase is a so-called charge-transfer insulator, not a Mott-Hubbard insulator. Using cluster dynamical mean-field theory with continuous-time quantum Monte Carlo as an impurity solver and 12 atoms per cluster, we report the normal and superconducting phase diagram of this model as a function of doping, interaction strength, and temperature. As expected, the three-orbital model is consistent with the experimental observation that doped holes are located predominantly on oxygens, a result that goes beyond the one-orbital model. Nevertheless, the phase boundary between pseudogap and correlated metal, the Widom line, and the origin of the pairing energy (kinetic vs potential) are similar to the one-orbital model, demonstrating that these are emergent phenomena characteristic of doped Mott insulators, independently of many microscopic details. Broader implications are discussed.
The three band Hubbard model with nearest neighbour repulsion is studied in the U=∞ limit using the large N expansion technique to order [Formula: see text]. A charge transfer (CT) instability is found like in weak coupling theory. However at small doping a major role is played by the Brinkman-Rice point. The CT instability is always associated with a diverging compressibility leading to a phase separation. The evaluation to order [Formula: see text] of the effective scattering amplitude in the Cooper channel shows the presence of superconducting instabilities in the s and d wave channel near the phase separation.
We analyze the role of the collective modes on the charge-transfer instability (CTI), phase separation, and the superconductivity in the extended Hubbard model. We show that, in the weak-coupling limit, the CTI appears when the zero-sound mode becomes unstable and the Landau stability criterion F0s{\mathit{F}}_{0}^{\mathit{s}}F0s​>-1 is violated, due to a coupling to the charge-transfer exciton. We also study the frequency dependence of the effective interaction, mediated by the exchange of collective modes, between the quasiparticles.
The phase diagram of the copper-oxide chain as a function of density and the nearest-neighbour Coulomb interaction, V , is determined. Phase separation takes place above a critical value of V when the Cu 2+ → Cu + valence fluctuations dominate. In the proximity of the phase separation boundary the superconducting correlations are the most divergent. We identify the parameter regions where the Luttinger-liquid theory applies and calculate the contours of the charge-charge correlation exponent K ρ . We show that anomalous flux quantization occurs as K ρ diverges. At n = 1, for V > t , a gap opens in the spectrum and the ground state is a charge density wave.