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Physical Review B

Bethe-Salpeter equations for the collective modes of the t−U−V−J model with d -wave pairing: Analysis of the photoemission resonance of Bi2Sr2CaCu2O8

Zlatko G. Koinov, Patrick L. Nash

Published Jul 21, 2010• 5 citations
Publisher

Abstract

The Bethe-Salpeter equations for the collective modes of a $t\text{\ensuremath{-}}U\text{\ensuremath{-}}V\text{\ensuremath{-}}J$ model are used to analyze the resonance peak observed at $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$ in neutron-scattering experiments on the cuprates. We assume that the resonance emerges due to the mixing between the spin channel and 19 other channels. We have calculated the energy of the lowest mode of the extended Hubbard model $(J=0)$ vs the on-site repulsive interaction $U$, as well as the $UJ$ lines in the interaction parameter space which are consistent with the angle-resolved photoemission spectroscopy data and reproduces the resonance peak at 40 meV in Bi2212 compound. We find that the resonance is predominantly a spin exciton.

DOI
10.1103/physrevb.82.014528

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The Bethe-Salpeter equations for the collective modes of a t\ensuremath-U\ensuremath-V\ensuremath-Jt\text{\ensuremath{-}}U\text{\ensuremath{-}}V\text{\ensuremath{-}}Jt\ensuremath-U\ensuremath-V\ensuremath-J model are used to analyze the resonance peak observed at Q=(\ensuremathπ,\ensuremathπ)\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})Q=(\ensuremathπ,\ensuremathπ) in neutron-scattering experiments on the cuprates. We assume that the resonance emerges due to the mixing between the spin channel and 19 other channels. We have calculated the energy of the lowest mode of the extended Hubbard model (J=0)(J=0)(J=0) vs the on-site repulsive interaction UUU, as well as the UJUJUJ lines in the interaction parameter space which are consistent with the angle-resolved photoemission spectroscopy data and reproduces the resonance peak at 40 meV in Bi2212 compound. We find that the resonance is predominantly a spin exciton.
Bethe-Salpeter equations for the collective modes of the t−U−V−Jt-U-V-Jt−U−V−J model with d-wave pairing
The Bethe-Salpeter equations for the collective modes of a ttt-UUU-VVV-JJJ model are used to analyze the resonance peak observed at Q=(π,π)\bf{Q}=(π,π)Q=(π,π) in neutron scattering experiments on the cuprates. We assume that the resonance emerges due to the mixing between the spin channel and 19 other channels. We have calculated the energy of the lowest mode of the extended Hubbard model (J=0J=0J=0) vs the on-site repulsive interaction UUU, as well as the UJUJUJ lines in the interaction parameter space which are consistent with the ARPES data and reproduces the resonance peak at 40 meV in Bi2212 compound. We find that the resonance is predominantly a spin exciton.
The Bethe-Salpeter equation is combined with the temperature-cutoff functional renormalization group approach to analyze the order parameter structure for the leading instabilities of the 2D $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model. We find significant deviations from the conventional sss-, ppp-, or ddd-wave forms, which is due to the frustration of antiferromagnetism at small and intermediate ${t}^{\ensuremath{'}}$. With adding a direct antiferromagnetic spin-exchange coupling the eigenfunctions in the particle-hole channel have extended sss-wave form, while in the particle-particle singlet pairing channel a higher angular momentum component arises besides the standard ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave component, which flattens the angular dependence of the gap. For ${t}^{\ensuremath{'}}$ closer to t∕2t∕2t∕2 we find a delicate competition of ferromagnetism and triplet pairing with a nontrivial pair-wavefunction.
We provide a unified interpretation of both paramagnon and plasmon modes in high-Tc{T}_{c}Tc​ copper-oxides, and verify it quantitatively against available resonant inelastic xxx-ray scattering (RIXS) data across the hole-doped phase diagram. The three-dimensional extended Hubbard model, with included long-range Coulomb interactions and doping-independent microscopic parameters for both classes of quantum fluctuations, is used. Collective modes are studied using VWF+1/Nf\mathrm{VWF}+1/{\mathcal{N}}_{f}VWF+1/Nf​ approach which extends variational wave function (VWF) scheme by means of an expansion in inverse number of fermionic flavors (1/Nf)(1/{\mathcal{N}}_{f})(1/Nf​). We show that intense paramagnons persist along the antinodal line from the underdoped to the overdoped regime and undergo rapid overdamping in the nodal direction. Plasmons exhibit a three-dimensional character, with minimal energy corresponding to antiphase oscillations on neighboring CuO2{\mathrm{CuO}}_{2}CuO2​ planes. The theoretical spin- and charge excitation energies reproduce semiquantitatively RIXS data for ${(\mathrm{Bi},\mathrm{Pb})}_{2}{(\mathrm{Sr},\mathrm{La})}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$. The present VWF+1/Nf\mathrm{VWF}+1/{\mathcal{N}}_{f}VWF+1/Nf​ analysis of dynamics and former VWF results for static quantities combine into a consistent description of the principal properties of hole-doped high-Tc{T}_{c}Tc​ cuprates as strongly correlated systems.
Pseudogap phenomena are observed for the normal underdoped phase of different high-T c cuprates. Among others, the Bi2Sr2CaCu2O8 − δ (Bi2212) compound is one of the most studied experimentally. To describe the pseudogap regime in Bi2212, we use a novel generalized ab initio LDA + DMFT + Σk hybrid scheme. This scheme is based on the strategy of one of the most powerful computational tools for real correlated materials: the local density approximation (LDA) + dynamical mean-field theory (DMFT). Conventional LDA + DMFT equations are here supplied with an additional (momentum-dependent) self-energy Σk in the spirit of our recently proposed DMFT + Σk approach taking into account pseudogap fluctuations. In the present model, Σk describes nonlocal correlations induced by short-range collective Heisenberg-like antiferromagnetic spin fluctuations. The effective single-impurity problem of the DMFT is solved by the numerical renormalization group (NRG) method. Material-specific model parameters for the effective x 2 − y 2 orbital of Cu-3d shell of the Bi2212 compound, e.g., the values of intra-and interlayer hopping integrals between different Cu sites, the local Coulomb interaction U, and the pseudogap potential Δ were obtained within the LDA and LDA + DMFT schemes. Here, we report on the theoretical LDA + DMFT + Σk quasiparticle band dispersion and damping, Fermi surface renormalization, momentum anisotropy of (quasi)static scattering, densities of states, spectral densities, and angular-resolved photoemission (ARPES) spectra, taking into account pseudogap and bilayer splitting effects for normal (slightly) underdoped Bi2212 (δ = 0.15). We show that LDA + DMFT + Σk successfully describes strong (pseudogap) scattering close to Brillouin zone boundaries. Our calculated LDA + DMFT + Σk Fermi surfaces and ARPES spectra in the presence of pseudogap fluctuations are almost insensitive to the bilayer splitting strength. However, our LDA-calculated value of bilayer splitting is rather small to describe the experimentally observed peak-dip-hump structure. The results obtained are in good semiquantitative agreement with various recent ARPES experiments.
The quasiparticle spectral function is calculated for the 2D Hubbard model of Bi2212 with n\ensuremath{\sim}0.9. For momenta k\ensuremath{\gtrsim}kF{\mathit{k}}_{\mathit{F}}kF​ we obtain dips and satellite peaks at energies \ensuremath{\omega}0 which are caused by strong scattering of quasiparticles on antiferromagnetic spin fluctuations. These structures, which may be observable, become very pronounced below Tc{\mathit{T}}_{\mathit{c}}Tc​ even for momenta k lying along the node of the ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$ wave gap. For k along the antinode of the gap we obtain below Tc{\mathit{T}}_{\mathit{c}}Tc​ a shift of the quasiparticle peak and a dip in qualitative agreement with ARPES measurements on Bi2212. \textcopyright{} 1996 The American Physical Society.
The t-J-U model of high-Tc copper-oxide superconductors incorporates both the on-site Coulomb repulsion and kinetic exchange interaction and yields a semi-quantitative description of the static properties of those materials. We extend this analysis to dynamic quantities and address collective spin- and charge excitations in the correlated metallic state of the t-J-U model. We employ VWF+1/Nf approach that combines the variational wave function (VWF) approach with the expansion in the inverse number of fermionic flavors (1/Nf). It is shown that the resonant (paramagnon) contribution to the dynamic magnetic susceptibility remains robust as one interpolates between the Hubbard- and t-J-model limits, whereas the incoherent continuum undergoes substantial renormalization. Energy of the collective charge mode diminishes as the strong-coupling limit is approached. We also introduce the concept of effective kinetic exchange interaction that allows for a unified interpretation of magnetic dynamics in the Hubbard, t-J, and t-J-U models. The results are discussed in the context of recent resonant inelastic x-ray scattering experiments for the high-Tc cuprates.