arXiv:2003.03117 · Physical review. B./Physical review. B

Superconducting properties of the hole-doped three-band d−p model studied with minimal-size real-space d -wave pairing operators

Andrzej Biborski, M. Zegrodnik, Józef Spałek

Published Jun 4, 2020• 12 citations

Abstract

The three-band d-p model is investigated by means of a variational Monte Carlo (VMC) method with the BCS-like wave-function supplemented by the Gutzwiller and Jastrow correlators. The VMC optimization leads to a $d\text{\ensuremath{-}}\mathit{wave}$ superconducting state with a characteristic domelike shape of the order parameter for hole doping $\ensuremath{\delta}\ensuremath{\lesssim}0.4$, in good agreement with the experimental observations. Also, the off-diagonal pair-pair correlation functions, calculated within VMC, vindicates the results obtained very recently within the diagrammatic expansion of the Gutzwiller wave function method [cf. Zegrodnik, Biborski, Fidrysiak, and Spa\l{}ek, Phys. Rev. B 99, 104511 (2019)]. Subsequently, the nature of the $d\text{\ensuremath{-}}\mathit{wave}$ pairing is investigated by means of recently proposed minimal-size real-space d-wave pairing operators [Moreo and Dagotto, Phys. Rev. B 100, 214502 (2019)]. An emergence of the long-range superconducting ordering for both $d$ and $p$ orbitals is reported by analyzing the corresponding off-diagonal pair-pair correlation functions. The dominant character of d-wave pairing on $d$ orbitals is confirmed. Additionally, the trial wave function is used to investigate the magnetic properties of the system. The analysis of spin-spin correlation functions is carried out and shows antiferromagnetic $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$, short-range order, as expected. For the sake of completeness, the charge gap has been estimated, which for the parent compound takes the value ${\mathrm{\ensuremath{\Delta}}}_{\text{CG}}\ensuremath{\approx}1.78\ifmmode\pm\else\textpm\fi{}0.51\phantom{\rule{4.pt}{0ex}}\text{eV}$, and agrees with values reported experimentally for the cuprates.

DOI: 10.1103/physrevb.101.214504

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Hole doped three-band \emph{d-p} model: Superconducting properties in view of minimal-size real-space $d$-wave pairing operators by means of Variational Monte-Carlo method

Andrzej Biborski, M. Zegrodnik, Józef Spałek

Mar 6, 20200 citations

Correlated-Electron Systems and High-Temperature Superconductivity

Takashi Yanagisawa, Mitake Miyazaki, Yamaji K.

arXiv:1307.2456Journal of Modern PhysicsJan 1, 201323 citations

Incorporation of charge- and pair-density-wave states into the one-band model of d -wave superconductivity

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Phase diagram of the three-band d-p model based on the optimization variational Monte Carlo method

Takashi Yanagisawa, Mitake Miyazaki, Yamaji K.

arXiv:2105.00464May 2, 20210 citations

Strongly correlated nature of d-wave superconductivity in cuprates

H. Yokoyama, Shun Tamura, T. Miyagawa +2 more

Physics ProcediaJan 1, 20121 citation

arXiv:2003.03117 · Physical review. B./Physical review. B

Superconducting properties of the hole-doped three-band d−p model studied with minimal-size real-space d -wave pairing operators

Andrzej Biborski, M. Zegrodnik, Józef Spałek

Published Jun 4, 2020• 12 citations

arXiv HTML PDF

Abstract

d\text{\ensuremath{-}}\mathit{wave}

superconducting state with a characteristic domelike shape of the order parameter for hole doping

\ensuremath{\delta}\ensuremath{\lesssim}0.4

, in good agreement with the experimental observations. Also, the off-diagonal pair-pair correlation functions, calculated within VMC, vindicates the results obtained very recently within the diagrammatic expansion of the Gutzwiller wave function method [cf. Zegrodnik, Biborski, Fidrysiak, and Spa\l{}ek, Phys. Rev. B 99, 104511 (2019)]. Subsequently, the nature of the

d\text{\ensuremath{-}}\mathit{wave}

pairing is investigated by means of recently proposed minimal-size real-space d-wave pairing operators [Moreo and Dagotto, Phys. Rev. B 100, 214502 (2019)]. An emergence of the long-range superconducting ordering for both

d

and

p

orbitals is reported by analyzing the corresponding off-diagonal pair-pair correlation functions. The dominant character of d-wave pairing on

d

orbitals is confirmed. Additionally, the trial wave function is used to investigate the magnetic properties of the system. The analysis of spin-spin correlation functions is carried out and shows antiferromagnetic

\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})

, short-range order, as expected. For the sake of completeness, the charge gap has been estimated, which for the parent compound takes the value

{\mathrm{\ensuremath{\Delta}}}_{\text{CG}}\ensuremath{\approx}1.78\ifmmode\pm\else\textpm\fi{}0.51\phantom{\rule{4.pt}{0ex}}\text{eV}

, and agrees with values reported experimentally for the cuprates.

DOI: 10.1103/physrevb.101.214504

Related papers

Hole doped three-band \emph{d-p} model: Superconducting properties in view of minimal-size real-space $d$ -wave pairing operators by means of Variational Monte-Carlo methodHole doped three-band \emph{d-p} model: Superconducting properties in view of minimal-size real-space $d$-wave pairing operators by means of Variational Monte-Carlo method

Andrzej Biborski, M. Zegrodnik, Józef Spałek

The three-band \emph{d-p} model is investigated by means of Variational Monte-Carlo method with the BCS-like wave-function supplemented with the Gutzwiller and Jastrow correlators. Optimization by means of Variational Monte-Carlo approach has lead to reproduction of the $d$ - $wave$ superconducting state with the characteristic dome-like shape of the order parameter for hole doping $\delta \lesssim 0.4$ with a good agreement with both the diagrammatic expansion of Gutzwiller wave-function (DE-GWF) method and the experimental observations. The nature of the $d$ - $wave$ pairing is also investigated by means of recently proposed \emph{Minimal-size real-space $d$ -wave pairing operators} [A. Moreo and E. Dagotto, Phys. Rev. B \textbf{100}, 214502 (2019)]. Simultaneous emergence of the long-range superconducting ordering observed by means of the correlation functions is reported. Additionally, the trial wave-function is used to investigate the magnetic properties of the system. The analysis of spin-spin correlation functions is carried out, resulting in the evidence of antiferromagnetic $\mathbf{q}=(\pi,\pi)$ , short-range order, as expected. For the sake of completeness, estimation of charge gap resulted in $\Delta_{CG}\approx1.2\text{eV}$ , which is close to values reported experimentally for cuprates.The three-band \emph{d-p} model is investigated by means of Variational Monte-Carlo method with the BCS-like wave-function supplemented with the Gutzwiller and Jastrow correlators. Optimization by means of Variational Monte-Carlo approach has lead to reproduction of the $d$-$wave$ superconducting state with the characteristic dome-like shape of the order parameter for hole doping $\delta \lesssim 0.4$ with a good agreement with both the diagrammatic expansion of Gutzwiller wave-function (DE-GWF) method and the experimental observations. The nature of the $d$-$wave$ pairing is also investigated by means of recently proposed \emph{Minimal-size real-space $d$-wave pairing operators} [A. Moreo and E. Dagotto, Phys. Rev. B \textbf{100}, 214502 (2019)]. Simultaneous emergence of the long-range superconducting ordering observed by means of the correlation functions is reported. Additionally, the trial wave-function is used to investigate the magnetic properties of the system. The analysis of spin-spin correlation functions is carried out, resulting in the evidence of antiferromagnetic $\mathbf{q}=(\pi,\pi)$, short-range order, as expected. For the sake of completeness, estimation of charge gap resulted in $\Delta_{CG}\approx1.2\text{eV}$, which is close to values reported experimentally for cuprates.

Mar 6, 20200 citations

Correlated-Electron Systems and High-Temperature Superconductivity

Takashi Yanagisawa, Mitake Miyazaki, Yamaji K.

We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.

arXiv:1307.2456Journal of Modern PhysicsJan 1, 201323 citations

Incorporation of charge- and pair-density-wave states into the one-band model of d -wave superconductivity

M. Zegrodnik, Józef Spałek

We study the coexistence of pair- (PDW) and charge-density-wave (CDW) states within the single-band $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ and Hubbard models of $d$ -wave superconductivity and discuss our results in the context of the experimental observations for the copper-based compounds. In order to take the correlation effects into account with proper precision, we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF), which goes beyond the renormalized mean-field theory in a systematic manner. According to our analysis of the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model, the transition between the pure $d$ -wave superconducting phase and the coexistent CDW+PDW phase takes place at $\ensuremath{\delta}\ensuremath{\approx}0.18$ (close to the optimal doping), with the modulated phase located in the underdoped regime. The situation is different for the case of the Hubbard model, where a narrow stability regime of a precursor nematic phase sets in preceding the formation of the modulated CDW+PDW state, with decreasing hole doping. The results conclude our comprehensive discussion of the standard phase diagram for high- ${T}_{C}$ superconducting compounds within the DE-GWF variational approach in the single narrow-band case [see J. Spa\l{}ek et al., Phys. Rev. B 95, 024506 (2017); M. Zegrodnik and Spa\l{}ek, Phys. Rev. B 95, 024507 (2017); Phys. Rev. B 96, 054511 (2017); New J. Phys. 20, 063015 (2018)].We study the coexistence of pair- (PDW) and charge-density-wave (CDW) states within the single-band $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ and Hubbard models of $d$-wave superconductivity and discuss our results in the context of the experimental observations for the copper-based compounds. In order to take the correlation effects into account with proper precision, we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF), which goes beyond the renormalized mean-field theory in a systematic manner. According to our analysis of the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model, the transition between the pure $d$-wave superconducting phase and the coexistent CDW+PDW phase takes place at $\ensuremath{\delta}\ensuremath{\approx}0.18$ (close to the optimal doping), with the modulated phase located in the underdoped regime. The situation is different for the case of the Hubbard model, where a narrow stability regime of a precursor nematic phase sets in preceding the formation of the modulated CDW+PDW state, with decreasing hole doping. The results conclude our comprehensive discussion of the standard phase diagram for high-${T}_{C}$ superconducting compounds within the DE-GWF variational approach in the single narrow-band case [see J. Spa\l{}ek et al., Phys. Rev. B 95, 024506 (2017); M. Zegrodnik and Spa\l{}ek, Phys. Rev. B 95, 024507 (2017); Phys. Rev. B 96, 054511 (2017); New J. Phys. 20, 063015 (2018)].

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Pairing, charge, and spin correlations in the three-band Hubbard model

Zhongbing Huang, Hua Lin, James E. Gubernatis

Using the constrained path Monte Carlo method, we simulated the two-dimensional, three-band Hubbard model to study pairing, charge, and spin correlations as a function of electron and hole doping and the Coulomb repulsion ${V}_{\mathrm{pd}}$ between charges on neighboring Cu and O lattice sites. As a function of distance, both the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and extended s-wave pairing correlations decayed quickly. In the charge-transfer regime, increasing ${V}_{\mathrm{pd}}$ decreased the long-range part of the correlation functions in both channels, while in the mixed-valent regime, it increased the long-range part of the s-wave behavior but decreased that of the d-wave behavior. Still the d-wave behavior dominated. At a given doping, increasing ${V}_{\mathrm{pd}}$ increased the spin-spin correlations in the charge-transfer regime but decreased them in the mixed-valent regime. Also, increasing ${V}_{\mathrm{pd}}$ suppressed the charge-charge correlations between neighboring Cu and O sites. Electron and hole doping away from half-filling was accompanied by a rapid suppression of antiferromagnetic correlations. Our results suggest that adding a repulsive ${V}_{\mathrm{pd}}$ to the model does not enhance its tendency toward superconductivity even though the behavior of the spin structure factor is consistent with the properties of some high-temperature superconducting materials.Using the constrained path Monte Carlo method, we simulated the two-dimensional, three-band Hubbard model to study pairing, charge, and spin correlations as a function of electron and hole doping and the Coulomb repulsion ${V}_{\mathrm{pd}}$ between charges on neighboring Cu and O lattice sites. As a function of distance, both the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and extended s-wave pairing correlations decayed quickly. In the charge-transfer regime, increasing ${V}_{\mathrm{pd}}$ decreased the long-range part of the correlation functions in both channels, while in the mixed-valent regime, it increased the long-range part of the s-wave behavior but decreased that of the d-wave behavior. Still the d-wave behavior dominated. At a given doping, increasing ${V}_{\mathrm{pd}}$ increased the spin-spin correlations in the charge-transfer regime but decreased them in the mixed-valent regime. Also, increasing ${V}_{\mathrm{pd}}$ suppressed the charge-charge correlations between neighboring Cu and O sites. Electron and hole doping away from half-filling was accompanied by a rapid suppression of antiferromagnetic correlations. Our results suggest that adding a repulsive ${V}_{\mathrm{pd}}$ to the model does not enhance its tendency toward superconductivity even though the behavior of the spin structure factor is consistent with the properties of some high-temperature superconducting materials.

arXiv:cond-mat/0009433Physical review. B, Condensed matterMar 1, 200128 citations

Phase diagram of the three-band d-p model based on the optimization variational Monte Carlo method

Takashi Yanagisawa, Mitake Miyazaki, Yamaji K.

The phase diagram of cuprate high-temperature superconductors is investigated on the basis of the three-band d-p model. We use the optimization variational Monte Carlo method, where improved many-body wave functions have been proposed to make the ground-state wave function more precise. We investigate the stability of antiferromagnetic state by changing the band parameters such as the hole number, level difference $Δ_{dp}$ between $d$ and $p$ electrons and transfer integrals. We show that the antiferromagnetic correlation weakens when $Δ_{dp}$ decreases and the pure $d$ -wave superconducting phase may exist in this region. We present phase diagrams including antiferromagnetic and superconducting regions by varying the band parameters. The phase diagram obtained by changing the doping rate $x$ contains antiferromagnetic, superconducting and also phase-separated phases. We propose that high-temperature superconductivity will occur near the antiferromagnetic boundary in the space of band parameters.The phase diagram of cuprate high-temperature superconductors is investigated on the basis of the three-band d-p model. We use the optimization variational Monte Carlo method, where improved many-body wave functions have been proposed to make the ground-state wave function more precise. We investigate the stability of antiferromagnetic state by changing the band parameters such as the hole number, level difference $Δ_{dp}$ between $d$ and $p$ electrons and transfer integrals. We show that the antiferromagnetic correlation weakens when $Δ_{dp}$ decreases and the pure $d$-wave superconducting phase may exist in this region. We present phase diagrams including antiferromagnetic and superconducting regions by varying the band parameters. The phase diagram obtained by changing the doping rate $x$ contains antiferromagnetic, superconducting and also phase-separated phases. We propose that high-temperature superconductivity will occur near the antiferromagnetic boundary in the space of band parameters.

arXiv:2105.00464May 2, 20210 citations

Strongly correlated nature of d-wave superconductivity in cuprates

H. Yokoyama, Shun Tamura, T. Miyagawa +2 more

With the high-Tc cuprates in mind, properties of correlated d-wave superconducting (SC) states are studied for a Hubbard model on square lattices with a diagonal transfer (t-t’-U model), using a variational Monte Carlo method. We employ a simple wave function, which includes crucial parameters, in particular, a doublon-holon (D-H) binding factor important for correlated SC and normal states as doped Mott insulators. We first check that the range of dominant superconductivity is limited to a strongly correlated regime (U>W, U: onsite correlation strength, W: band width), and coincides with the effective range of the D-H binding factors. In this range of U/t and δ (doping rate), holons (in hole-doped cases) are classified into two types: doped holons and ones created as D-H pairs. Only the former holons participate in current, whereas the latter contribute to singlet-pair formation. Next, we show that the SC properties undergo a crossover at U=Uco∼W. For U<Uco, the behavior is appropriately interpreted with the conventional BCS mechanism, whereas for U>Uco (the regime of cuprates), a new idea is needed to understand the peculiar SC behavior.With the high-Tc cuprates in mind, properties of correlated d-wave superconducting (SC) states are studied for a Hubbard model on square lattices with a diagonal transfer (t-t’-U model), using a variational Monte Carlo method. We employ a simple wave function, which includes crucial parameters, in particular, a doublon-holon (D-H) binding factor important for correlated SC and normal states as doped Mott insulators. We first check that the range of dominant superconductivity is limited to a strongly correlated regime (U>W, U: onsite correlation strength, W: band width), and coincides with the effective range of the D-H binding factors. In this range of U/t and δ (doping rate), holons (in hole-doped cases) are classified into two types: doped holons and ones created as D-H pairs. Only the former holons participate in current, whereas the latter contribute to singlet-pair formation. Next, we show that the SC properties undergo a crossover at U=Uco∼W. For U<Uco, the behavior is appropriately interpreted with the conventional BCS mechanism, whereas for U>Uco (the regime of cuprates), a new idea is needed to understand the peculiar SC behavior.

Physics ProcediaJan 1, 20121 citation

d\text{\ensuremath{-}}\mathit{wave}

superconducting state with a characteristic domelike shape of the order parameter for hole doping

\ensuremath{\delta}\ensuremath{\lesssim}0.4

d\text{\ensuremath{-}}\mathit{wave}

d

and

p

orbitals is reported by analyzing the corresponding off-diagonal pair-pair correlation functions. The dominant character of d-wave pairing on

d

\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})

, short-range order, as expected. For the sake of completeness, the charge gap has been estimated, which for the parent compound takes the value

{\mathrm{\ensuremath{\Delta}}}_{\text{CG}}\ensuremath{\approx}1.78\ifmmode\pm\else\textpm\fi{}0.51\phantom{\rule{4.pt}{0ex}}\text{eV}

, and agrees with values reported experimentally for the cuprates.

Hole doped three-band \emph{d-p} model: Superconducting properties in view of minimal-size real-space

d

-wave pairing operators by means of Variational Monte-Carlo method

d

wave

superconducting state with the characteristic dome-like shape of the order parameter for hole doping

\delta \lesssim 0.4

with a good agreement with both the diagrammatic expansion of Gutzwiller wave-function (DE-GWF) method and the experimental observations. The nature of the

d

wave

pairing is also investigated by means of recently proposed \emph{Minimal-size real-space

d

-wave pairing operators} [A. Moreo and E. Dagotto, Phys. Rev. B \textbf{100}, 214502 (2019)]. Simultaneous emergence of the long-range superconducting ordering observed by means of the correlation functions is reported. Additionally, the trial wave-function is used to investigate the magnetic properties of the system. The analysis of spin-spin correlation functions is carried out, resulting in the evidence of antiferromagnetic

\mathbf{q}=(\pi,\pi)

, short-range order, as expected. For the sake of completeness, estimation of charge gap resulted in

\Delta_{CG}\approx1.2\text{eV}

, which is close to values reported experimentally for cuprates.

We study the coexistence of pair- (PDW) and charge-density-wave (CDW) states within the single-band $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ and Hubbard models of

d

-wave superconductivity and discuss our results in the context of the experimental observations for the copper-based compounds. In order to take the correlation effects into account with proper precision, we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF), which goes beyond the renormalized mean-field theory in a systematic manner. According to our analysis of the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model, the transition between the pure

d

-wave superconducting phase and the coexistent CDW+PDW phase takes place at $\ensuremath{\delta}\ensuremath{\approx}0.18$ (close to the optimal doping), with the modulated phase located in the underdoped regime. The situation is different for the case of the Hubbard model, where a narrow stability regime of a precursor nematic phase sets in preceding the formation of the modulated CDW+PDW state, with decreasing hole doping. The results conclude our comprehensive discussion of the standard phase diagram for high-

{T}_{C}

superconducting compounds within the DE-GWF variational approach in the single narrow-band case [see J. Spa\l{}ek et al., Phys. Rev. B 95, 024506 (2017); M. Zegrodnik and Spa\l{}ek, Phys. Rev. B 95, 024507 (2017); Phys. Rev. B 96, 054511 (2017); New J. Phys. 20, 063015 (2018)].

{V}_{\mathrm{pd}}

between charges on neighboring Cu and O lattice sites. As a function of distance, both the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and extended s-wave pairing correlations decayed quickly. In the charge-transfer regime, increasing

{V}_{\mathrm{pd}}

decreased the long-range part of the correlation functions in both channels, while in the mixed-valent regime, it increased the long-range part of the s-wave behavior but decreased that of the d-wave behavior. Still the d-wave behavior dominated. At a given doping, increasing

{V}_{\mathrm{pd}}

increased the spin-spin correlations in the charge-transfer regime but decreased them in the mixed-valent regime. Also, increasing

{V}_{\mathrm{pd}}

suppressed the charge-charge correlations between neighboring Cu and O sites. Electron and hole doping away from half-filling was accompanied by a rapid suppression of antiferromagnetic correlations. Our results suggest that adding a repulsive

{V}_{\mathrm{pd}}

to the model does not enhance its tendency toward superconductivity even though the behavior of the spin structure factor is consistent with the properties of some high-temperature superconducting materials.

Δ_{dp}

between

d

and

p

electrons and transfer integrals. We show that the antiferromagnetic correlation weakens when

Δ_{dp}

decreases and the pure

d

-wave superconducting phase may exist in this region. We present phase diagrams including antiferromagnetic and superconducting regions by varying the band parameters. The phase diagram obtained by changing the doping rate

x

contains antiferromagnetic, superconducting and also phase-separated phases. We propose that high-temperature superconductivity will occur near the antiferromagnetic boundary in the space of band parameters.