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arXiv:cond-mat/9609219 · Physical Review Letters

Comment on “Quantum Monte Carlo Evidence for Superconductivity in the Three-Band Hubbard Model in Two Dimensions”

H. Endres, Werner R. Hanke, Hans Gerd Evertz, Fakher F. Assaad

Published Jan 6, 1997• 6 citations
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Abstract

In a recent Letter, Kuroki and Aoki [Phys. Rev. Lett. 76, 440 (1996)] presented quantum Monte-Carlo (QMC) results for pairing correlations in the three-band Hubbard model, which describes the Cu-d_{x^2-y^2} and O-p_{x,y} orbitals present in the CuO_2 planes of high-T_c materials. In this comment we argue that (i) the used parameter set is not appropriate for the description of high-T_c materials since it does not satisfy the minimal requirement of a charge-transfer gap at half-filling, and (ii) the observed increase in the d_{x^2-y^2} channel is dominantly produced by the pair-field correlations without the vertex part. Hence, the claim of evidence of ODLRO is not justified.

DOI
10.1103/physrevlett.78.160

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In a recent Letter, Kuroki and Aoki [Phys. Rev. Lett. 76, 440 (1996)] presented quantum Monte-Carlo (QMC) results for pairing correlations in the three-band Hubbard model, which describes the Cu-d_{x^2-y^2} and O-p_{x,y} orbitals present in the CuO_2 planes of high-T_c materials. In this comment we argue that (i) the used parameter set is not appropriate for the description of high-T_c materials since it does not satisfy the minimal requirement of a charge-transfer gap at half-filling, and (ii) the observed increase in the d_{x^2-y^2} channel is dominantly produced by the pair-field correlations without the vertex part. Hence, the claim of evidence of ODLRO is not justified.
A possibility of the electronic origin of the high-temperature superconductivity in cuprates is probed with the quantum Monte Carlo method by revisiting the three-band Hubbard model comprising Cu ${3d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ and O ${2p}_{\ensuremath{\sigma}}$ orbitals. The ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ pairing correlation is found to turn into an increasing function of the repulsion Ud{U}_{d}Ud​ within the ddd orbitals or the ddd- ppp level offset $\ensuremath{\Delta}\ensuremath{\varepsilon}$, where the normalized correlation grows with the system size. We have detected this in both the charge-transfer and Mott-Hubbard regimes upon entering the strong-correlation region ( Ud{U}_{d}Ud​ or $\ensuremath{\Delta}\ensuremath{\varepsilon}>$ bare bandwidth).
The nature of the pairing mechanism responsible for high-temperature superconductivity remains a central theoretical puzzle in condensed matter physics. Here we discuss the properties of the two-dimensional CuO 2 layers common to these materials in terms of a three- band Hubbard model. We describe how recently devel oped quantum Monte Carlo simulation techniques al low one to calculate the physical properties of strongly interacting many-electron systems and discuss the re sources required for such simulations. Then we review what we have learned from these simulations about the antiferromagnetic, charge-transfer, and supercon ducting correlations in the three-band Hubbard model. We conclude with a discussion of future goals.
We present in this article results of Quantum Monte Carlo simulations for the three-band Hubbard model obtained both with the grand canonical approach as well as with the T =0 formalism. A direct comparison of Quantum Monte Carlo results with experimental values for the charge-transfer gap leads to a set of parameters for the three-band Hubbard model that consistently describes salient features of the high- T c superconductors. We find long-range antiferromagnetic order in the undoped case as well as an incommensurate structure for a doping concentration of δ≈0.20. Moreover the magnetic susceptibility as a function of doping δ is in a qualitative agreement with experiments. Concerning dynamical properties, we have evaluated the spectral density [Formula: see text]. The dispersion of the state with the lowest excitation energy is in very good agreement with experimental photoemission and inverse photoemission experiments for a doping concentration of δ=0.25. In the superconducting regime, we find that the interaction vertex for the pairing correlation function in the extended s-channel shows a maximum for δ~0.20, resembling the dependence of T c on doping. This feature is not present for other symmetries of the order parameter or in other parameter regions.
The nature of the pairing mechanism responsible for high-temperature superconductivity remains a central theoretical puzzle in condensed matter physics. In this paper the authors discuss the properties of the two-dimensional CuO{sub 2} layers common to these materials in terms of a three-bank Hubbard model. The authors describe how recently developed quantum Monte Carlo simulation techniques allow one to calculate the physical properties of strongly interacting many-electron systems and discuss the resources required for such simulations. Then the authors review what we have learned from these simulations about the antiferromagnetic, charge-transfer, and superconducting correlations in the three-band Hubbard model. The authors conclude with a discussion of future goals.
The observed magnetic spin susceptibility of high-temperature superconductors such as ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​ increases when x increases from zero, i.e., as one dopes away from half-filling. Recent Monte Carlo simulations of A. Moreo [Phys. Rev. B 48, 3380 (1993)] suggest that this behavior can be reproduced by the two-dimensional Hubbard model only at large coupling, namely, U/t of order 10. Using longer runs, our Monte Carlo simulations show that the same behavior as for U/t=10 is obtained even in the intermediate coupling regime (U/t=4), as long as the temperature is low enough (T=t/6) that strong antiferromagnetic correlations are building up at half-filling. These results are consistent with the fact that in two dimensions, the generalized random phase approximation should fail in the parameter range where it predicts a magnetic phase transition.
The quantum Monte Carlo method is used to reexamine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a ``correlated pairing,'' 〈c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\uparrow}}}$c-${\mathrm{tilde}}_{{\mathrm{i}}^{|\mathrm{I}\mathrm{H}}\mathrm{\ensuremath{\downarrow}}}$〉 with c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$\ensuremath{\equiv}${\mathrm{c}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$(1-${\mathrm{n}}_{\mathrm{i}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$), which is inferred from the t-J model, the strong-coupling limit of the Hubbard model. The pairing in the d-wave channel is found to possess both a divergence like 1/T in the pairing susceptibility and a growth of the ground-state pairing correlation with sample size, indicating an off-diagonal long-range order near (but not exactly at) half-filling.