arXiv:cond-mat/0007069 · Physical review. B, Condensed matter

Local properties and density of states in the two-dimensional p−d model of high- Tc superconductors

V. Fiorentino, Francesco Paolo Mancini, Ernestas Žąsinas, А. Ф. Барабанов

Published Nov 13, 2001• 10 citations

Abstract

The $p\ensuremath{-}d$ model which well describes the ${\mathrm{CuO}}_{2}$ planes of the high-${T}_{c}$ superconductors is studied by means of the composite operator method. The relevant quasiparticle excitations are represented by composite operators. As a result of taking into account spin excitations we find a p-like band near the Fermi level. The dispersion of this band gives a Fermi surface which is in good agreement with the experimental measurements. Due to the strong mixing of the relevant excitations, the spectral weight of this band is reduced and gives a large Fermi surface in the moderately doped region. The dependence of the calculated physical quantities on model parameters, temperature and doping, is in very good agreement with the available quantum Monte Carlo results.

DOI: 10.1103/physrevb.64.214515

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arXiv:cond-mat/0007069 · Physical review. B, Condensed matter

Local properties and density of states in the two-dimensional p−d model of high- Tc superconductors

V. Fiorentino, Francesco Paolo Mancini, Ernestas Žąsinas, А. Ф. Барабанов

Published Nov 13, 2001• 10 citations

arXiv HTML PDF

Abstract

The

p\ensuremath{-}d

model which well describes the

{\mathrm{CuO}}_{2}

planes of the high-

{T}_{c}

superconductors is studied by means of the composite operator method. The relevant quasiparticle excitations are represented by composite operators. As a result of taking into account spin excitations we find a p-like band near the Fermi level. The dispersion of this band gives a Fermi surface which is in good agreement with the experimental measurements. Due to the strong mixing of the relevant excitations, the spectral weight of this band is reduced and gives a large Fermi surface in the moderately doped region. The dependence of the calculated physical quantities on model parameters, temperature and doping, is in very good agreement with the available quantum Monte Carlo results.

DOI: 10.1103/physrevb.64.214515

Related papers

Superconductivity in the two-dimensional Hubbard model

J. Beenen, David M. Edwards

Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature ${\mathit{T}}_{\mathit{c}}$ is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/ ${\mathit{kT}}_{\mathit{c}}$ \ensuremath{\simeq}4.Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature ${\mathit{T}}_{\mathit{c}}$ is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/${\mathit{kT}}_{\mathit{c}}$\ensuremath{\simeq}4.

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The two-dimensional Hubbard model is studied within the composite operator method (COM) with the self-energy computed in the self-consistent Born approximation (SCBA). The COM describes interacting electrons in terms of the new elementary excitations that appear in the system owing to strong correlations; residual interactions among these excitations are treated within the SCBA. On decreasing the doping (from the overdoped to underdoped region), anomalous features develop in the spectral function $A(\mathbf{k},\ensuremath{\omega})$, the Fermi surface, the momentum distribution function $n(\mathbf{k})$ , the dispersion, and the density of states $N(\ensuremath{\omega})$ in the intermediate-coupling regime $(U=8)$ at low temperatures $(T=0.01--0.02)$ . At high doping $(n=0.7)$ , the system resembles an ordinary weakly interacting metal. At low doping $(n=0.92)$ , a pseudogap opens, hot and cold spots appear, and non-Fermi-liquid features develop. This behavior, together with the presence of kinks in the calculated electronic dispersion, is in agreement with angle-resolved photoemission spectroscopy data for high- ${T}_{c}$ cuprates superconductors.The two-dimensional Hubbard model is studied within the composite operator method (COM) with the self-energy computed in the self-consistent Born approximation (SCBA). The COM describes interacting electrons in terms of the new elementary excitations that appear in the system owing to strong correlations; residual interactions among these excitations are treated within the SCBA. On decreasing the doping (from the overdoped to underdoped region), anomalous features develop in the spectral function $A(\mathbf{k},\ensuremath{\omega})$, the Fermi surface, the momentum distribution function $n(\mathbf{k})$, the dispersion, and the density of states $N(\ensuremath{\omega})$ in the intermediate-coupling regime $(U=8)$ at low temperatures $(T=0.01--0.02)$. At high doping $(n=0.7)$, the system resembles an ordinary weakly interacting metal. At low doping $(n=0.92)$, a pseudogap opens, hot and cold spots appear, and non-Fermi-liquid features develop. This behavior, together with the presence of kinks in the calculated electronic dispersion, is in agreement with angle-resolved photoemission spectroscopy data for high-${T}_{c}$ cuprates superconductors.

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Hideki Matsumoto, Taiichiro Saikawa, Ferdinando Mancini

The temperature dependence of electronic states in the t-J model is studied in the moderately doped region by use of the composite operator method. Self-energy effects are included in two-site approximation. At higher temperature, the density of states shows a two-peak structure, and the coherent peak at the Fermi level increases its intensity with decreasing temperature. The peak at the Fermi level splits into two peaks with further decreasing temperature, corresponding to the electronic excitations from spin-singlet and -triplet states of the nearest-neighbor electrons. Electronic excitations from the singlet states form a narrower band at the Fermi level. This may relate to the spin gap formation observed in high- ${\mathit{T}}_{\mathit{c}}$ superconductors. \textcopyright{} 1996 The American Physical Society.The temperature dependence of electronic states in the t-J model is studied in the moderately doped region by use of the composite operator method. Self-energy effects are included in two-site approximation. At higher temperature, the density of states shows a two-peak structure, and the coherent peak at the Fermi level increases its intensity with decreasing temperature. The peak at the Fermi level splits into two peaks with further decreasing temperature, corresponding to the electronic excitations from spin-singlet and -triplet states of the nearest-neighbor electrons. Electronic excitations from the singlet states form a narrower band at the Fermi level. This may relate to the spin gap formation observed in high-${\mathit{T}}_{\mathit{c}}$ superconductors. \textcopyright{} 1996 The American Physical Society.

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V. А. Kashurnikov, Yu. G. Kharchenko

The spectral density of states for a 108-site Cu36O72 cluster in the two-dimensional three-band Emery model is reconstructed with the aid of a path integral Monte Carlo algorithm. Dispersion relations are obtained for quasiparticles in the upper Hubbard band and in the correlated-states band; this corresponds to electron and hole doping of high-T c superconductors. The form of the isoenergy surfaces is close to the experimentally observed form and confirms the existence of singularities in the density of states near the Fermi level.The spectral density of states for a 108-site Cu36O72 cluster in the two-dimensional three-band Emery model is reconstructed with the aid of a path integral Monte Carlo algorithm. Dispersion relations are obtained for quasiparticles in the upper Hubbard band and in the correlated-states band; this corresponds to electron and hole doping of high-T c superconductors. The form of the isoenergy surfaces is close to the experimentally observed form and confirms the existence of singularities in the density of states near the Fermi level.

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Theory for the Excitation Spectrum of High- Tc Superconductors: Quasiparticle Dispersion and Shadows of the Fermi Surface

Marcel Langer, Jörg Schmalian, Slawomir Janusz Grabowski +1 more

Using a new method for the solution of the fluctuation exchange approximation equations, which allows the determination of the self-energy ${\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$ of the 2D one-band Hubbard model on the real frequency axis, we calculate the doping dependence of the quasiparticle excitations of high- ${T}_{c}$ superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasiparticle dispersion, an anomalous $\ensuremath{\omega}$ dependence of $\mathrm{Im}{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$, and a related violation of the Luttinger theorem. This sheds new light on the influence of short range magnetic order on the low energy excitations and its significance for photoemission experiments.Using a new method for the solution of the fluctuation exchange approximation equations, which allows the determination of the self-energy ${\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$ of the 2D one-band Hubbard model on the real frequency axis, we calculate the doping dependence of the quasiparticle excitations of high-${T}_{c}$ superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasiparticle dispersion, an anomalous $\ensuremath{\omega}$ dependence of $\mathrm{Im}{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$, and a related violation of the Luttinger theorem. This sheds new light on the influence of short range magnetic order on the low energy excitations and its significance for photoemission experiments.

arXiv:cond-mat/9505063Physical Review LettersDec 11, 1995125 citations

The

p\ensuremath{-}d

model which well describes the

{\mathrm{CuO}}_{2}

planes of the high-

{T}_{c}

{\mathit{T}}_{\mathit{c}}

is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/

{\mathit{kT}}_{\mathit{c}}

\ensuremath{\simeq}4.

T_{\rm c}

cuprates.

n(\mathbf{k})

, the dispersion, and the density of states $N(\ensuremath{\omega})$ in the intermediate-coupling regime

(U=8)

at low temperatures

(T=0.01--0.02)

. At high doping

(n=0.7)

, the system resembles an ordinary weakly interacting metal. At low doping

(n=0.92)

, a pseudogap opens, hot and cold spots appear, and non-Fermi-liquid features develop. This behavior, together with the presence of kinks in the calculated electronic dispersion, is in agreement with angle-resolved photoemission spectroscopy data for high-

{T}_{c}

cuprates superconductors.

{\mathit{T}}_{\mathit{c}}

superconductors. \textcopyright{} 1996 The American Physical Society.

{T}_{c}

superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasiparticle dispersion, an anomalous $\ensuremath{\omega}$ dependence of $\mathrm{Im}{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$, and a related violation of the Luttinger theorem. This sheds new light on the influence of short range magnetic order on the low energy excitations and its significance for photoemission experiments.