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Journal of the Physical Society of Japan

Superconductivity of the One-Dimensionald-pModel withp-pTransfer. II

Kazuhiro Sano, Yoshiaki Ōno

Published Dec 15, 1998• 6 citations
Publisher

Abstract

We investigate the one-dimensional d - p model with the transfer energy t p p between the nearest neighbor p sites by the numerical diagonalization method. By calculating the critical exponent K ρ based on the Luttinger liquid relations and the paring correlation functions, we analyze the superconducting state induced by the effect of the large repulsion U d at the Cu site in cooperation with the transfer energy t p p . We obtain a phase diagram of the superconducting region on the filling n vs. U d parameter plane. It shows that the superconducting region appears when U d is larger than a certain critical value which decreases with increasing n . The results of paring correlation functions suggest that a singlet paring between the nearest neighbor p sites is most relevant to the superconductivity. We also discuss a relationship between the d - p model and the t - J model through an analysis of the dependence of K ρ on the parameters.

DOI
10.1143/jpsj.67.4151

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•Mar 23, 2007•0 citations
We investigate the one-dimensional d - p model with the transfer energy t p p between the nearest neighbor p sites by the numerical diagonalization method. By calculating the critical exponent K ρ based on the Luttinger liquid relations and the paring correlation functions, we analyze the superconducting state induced by the effect of the large repulsion U d at the Cu site in cooperation with the transfer energy t p p . We obtain a phase diagram of the superconducting region on the filling n vs. U d parameter plane. It shows that the superconducting region appears when U d is larger than a certain critical value which decreases with increasing n . The results of paring correlation functions suggest that a singlet paring between the nearest neighbor p sites is most relevant to the superconductivity. We also discuss a relationship between the d - p model and the t - J model through an analysis of the dependence of K ρ on the parameters.
Using the numerical diagonalization method, we investigate the one-dimensional ddd-ppp model, simulating a Cu-O linear chain with strong Coulomb repulsions. Paying attention to the effect of the transfer energy tppt_{pp}tpp​ between the nearest neighbor oxygen-sites, we calculate the critical exponent of correlation functions KρK_ρKρ​ based on the Luttinger liquid relations and the ground state energy E0(ϕ)E_0(ϕ)E0​(ϕ) as a function of an external flux ϕϕϕ. We find that the transfer tppt_{pp}tpp​ increases the charge susceptibility and the exponent KρK_ρKρ​ in cooperation with the repulsion UdU_{d}Ud​ at Cu-site. We also show that anomalous flux quantization occurs for Kρ>1K_ρ>1Kρ​>1. The superconducting region is presented on a phase diagram of UdU_{d}Ud​ vs. tppt_{pp}tpp​ plane.
In the present work the Roth s two-pole approximation (Phys. Rev. 184, 451 (1969)) has been used to investigate the role of d− p hybridization in the normal and superconducting states of an extended d− p Hubbard model. Superconductivity with singlet dx2−y2 -wave pairing is treated by following Beenen and Edwards formalism (Phys. Rev. B 52, 13636 (1995)). In the first part of this work, the effects of the hybridization on the superconductivity, in the hole-doped regime, have been studied treating Roth s band shift within two different approximations. In the first one, the band shift has been calculated in the limit U →¥ (U is the Coulomb interaction), with zero temperature and without consider the superconducting effects. These regards, are restrict to the band shift. In the other parts of the problem, U, the temperature and the superconducting effects have been considered finites. In the second approximation, the Coulomb interaction, the temperature and the superconductivity have been considered in the calculation of some relevant correlation functions present in the Roth s band shift. The obtained results show that the hybridization acts in the sense of to suppresses the superconductivity. Also, it has been verified that the first approximation overstimates the effects of the hybridization on the superconductivity. In the second part of these work, hoppings to second-nearest-neighbors have been included in the model with the purpose of reproduces adequately the asymetries (mainly those related with the Fermi surface, band structure and phase diagram) between the hole- and electron-doped systems. Particularly, it is shown that the crossover from hole-like to electronlike Fermi surface is deeply affected by the d − p hybridization in the hole doping case. It has been verified that the effect of the hybridization is most pronounced around the saddle-points, where the superconducting gap is maximum in the particular case of dx2−y2 -wave symmetry. As a consequence, the critical temperature Tc is directly affected by the hibridization. Moreover, the obtained results suggest that in the hole doped regime, the hybridization may act on the transport properties of the system due to the sign changes of the Hall coefficient when the crossover of the Fermi surface occurs. In the electron doped case, the crossover in the Fermi surface is not verified. Nevertheless, as the hybridization suppresses the density of states near the Fermi level, the superconductivity is affected. The topology of the Fermi surface in the hole and electron doping regime agree with recent experimental ARPES results for La2−xSrxCuO4 (hole doping) and Nd2−xCexCuO4 (electron doping).
We investigate the one-dimensional (1D) d-p model, simulating a Cu-O linear chain with strong Coulomb repulsion, by using the numerical diagonalization method. Using the Luttinger liquid theory, we obtained phase diagrams of the ground state on Ud{\mathit{U}}_{\mathit{d}}Ud​-Upd{\mathit{U}}_{\mathit{p}\mathit{d}}Upd​ plane, where Ud{\mathit{U}}_{\mathit{d}}Ud​ and Upd{\mathit{U}}_{\mathit{p}\mathit{d}}Upd​ represent on-site interaction at d sites and the nearest-neighbor interaction between p and d sites, respectively. In the weak-coupling region, they agree with the g-ology; a superconducting phase [SC(I)] is restricted to attractive interaction ${\mathit{U}}_{\mathit{p}\mathit{d}}$0. On the other hand, in the strong-coupling region, we found a superconducting phase [SC(II)] for repulsive interaction Upd{\mathit{U}}_{\mathit{p}\mathit{d}}Upd​>\ensuremath{\Vert}Ud{\mathit{U}}_{\mathit{d}}Ud​\ensuremath{\Vert} and an insulating state with a charge gap for Ud{\mathit{U}}_{\mathit{d}}Ud​>Udc{\mathit{U}}_{\mathit{d}}^{\mathit{c}}Udc​ and Upd{\mathit{U}}_{\mathit{p}\mathit{d}}Upd​>Updc{\mathit{U}}_{\mathit{p}\mathit{d}}^{\mathit{c}}Updc​ with critical values Udc{\mathit{U}}_{\mathit{d}}^{\mathit{c}}Udc​ and Updc{\mathit{U}}_{\mathit{p}\mathit{d}}^{\mathit{c}}Updc​ at half-filling. Away from half-filling, another superconducting phase [SC(III)] appears for Ud{\mathit{U}}_{\mathit{d}}Ud​\ensuremath{\gg}Upd{\mathit{U}}_{\mathit{p}\mathit{d}}Upd​>0; which has been found for Ud{\mathit{U}}_{\mathit{d}}Ud​\ensuremath{\rightarrow}\ensuremath{\infty} in the previous paper [Physica C 205, 170 (1993)]. An analysis of the spin gap suggests that the SC(I) and SC(II) include the Luther-Emery region (with spin gap) in part, while the SC(III) belongs to the Tomonaga-Luttinger region (without spin gap) in whole.
Using the numerical diagonalization method, we investigate superconductivity and related ferromagnetism in the one-dimensional two-orbital Hubbard model with a finite band splitting at less than half filling. We obtain superconducting (SC) region with the Luttinger liquid parameter Kρ > 1 and confirm anomalous flux quantization in the SC state. It is found that the SC phase appears near partially polarized ferromagnetic phase. We also calculate various pairing correlation functions to clarify the nature of the SC phase. Detailed analysis of these functions indicates that the triplet pairing between the nearest neighbor sites is relevant to the superconductivity. It suggests that the ferromagnetic fluctuation plays an important role for the superconductivity.