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Physical review. B, Condensed matter

Charge collective modes and dynamic pairing in the three-band Hubbard model. I. Weak-coupling limit

Yunkyu Bang, Gabriel Kotliar, Roberto Raimondi, Claudio Castellani, M. Grilli

Published Feb 1, 1993• 20 citations
Publisher

Abstract

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 ${\mathit{F}}_{0}^{\mathit{s}}$>-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.

DOI
10.1103/physrevb.47.3323

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•Jan 1, 1992•0 citations
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.
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.
We discuss the density-density response functions and the collective excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state.For the short-range intersite interaction we find the sound wave-like modes with the velocity interpolating smoothly between the weak (v 2Zt, |UD <2Zt) and strong coupling (v > 2Zt) limits.The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong coupling limit.In the weak coupling regime, we obtain that apart from a commensurate charge density wave instability, an increase in the intersite Coułomb repulsion can give rise to a charge density wave incommensurate with the lattice period, away from half-frlling.The ground state phase diagram for 2D square lattice, including singlet superconducting ground state, electronic droplet formation, and charge density waves is determined.It is also shown that the energy of collective excitations evolves smoothly from weak to strong coupling limit for a 2D lattice, in the case of a long-range Coulomb interaction.Finally, the mode coupling effects in the frequency behavior of the density-density response functions are analyzed.
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 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.
The auxiliary boson method and 1/N expansion are applied to the solution of the Hubbard model in the U = ∞\infty∞ limit, in functional integral form. The zero order term in the expansion gives the mean-field result of non-interacting enhanced mass quasiparticles, and the next order gives Gaussian fluctuations around the mean-field value, representing effective interactions between the quasiparticles. From the density-density correlation function, the collective mode indicates a very different behavior away from and close to half filling. The superconducting instability is examined to 1/$N\sp2$ order from the dominant double collective mode exchange. For a parabolic band, there is a p-wave triplet instability. But for a 2D square lattice, there is no superconducting pairing to this order. The effects of disorder on this system are also investigated. For moderate filling, the specific heat and scattering rate have the same results as predicted in the weakly interacting theories. Close to half-filling, the specific heat and scattering rate show a much sharper temperature and energy dependence.