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arXiv:cond-mat/9708230 · Journal of the Physical Society of Japan

Superconductivity of the One-Dimensionald-pModel withp-pTransfer

Kazuhiro Sano, Yoshiaki Ōno

Published Feb 15, 1998• 7 citations
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Abstract

Using the numerical diagonalization method, we investigate the one-dimensional $d$-$p$ model, simulating a Cu-O linear chain with strong Coulomb repulsions. Paying attention to the effect of the transfer energy $t_{pp}$ between the nearest neighbor oxygen-sites, we calculate the critical exponent of correlation functions $K_ρ$ based on the Luttinger liquid relations and the ground state energy $E_0(ϕ)$ as a function of an external flux $ϕ$. We find that the transfer $t_{pp}$ increases the charge susceptibility and the exponent $K_ρ$ in cooperation with the repulsion $U_{d}$ at Cu-site. We also show that anomalous flux quantization occurs for $K_ρ>1$. The superconducting region is presented on a phase diagram of $U_{d}$ vs. $t_{pp}$ plane.

DOI
10.1143/jpsj.67.389

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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.
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.
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.
The phase diagram of the copper-oxide chain as a function of density and the nearest-neighbour Coulomb interaction, V, is determined. Phase separation takes place above a critical value of VVV when the Cu2+ to Cu+ valence fluctuations dominate. In the proximity of the phase separation boundary the superconducting correlations are the most divergent. We identify the parameter regions where the Luttinger Liquid theory applies and calculate the contours of the charge-charge correlation exponent K_ρ. We show that anomalous flux quantization occurs as K_ρ diverges. At n = 1, for V > t, a gap opens in the spectrum and the ground state is a charge-density wave.
We examine effective interactions of the 1D d-p model mapped to a typical one-dimensional(1D) model such as the Hubbard model or the t-J model by the numerical diagonalization method combined with the Luttinger liquid theory. Analysis of the effective coupling constants of the mapped model gives the relationship between these models without ambiguity. We find that the renormalized interaction is relatively weak, though the repulsion of the d-p model at Cu-sites is very strong. We also find that the d-p model corresponds to not the t-J model but the Hubbard model for wide range of the parameters. It suggests that the Hubbard model is more favorable than the t-J model as a effective model of the d-p model in the low energy limit.
The exact ground-state energy E0{\mathit{E}}_{0}E0​(\ensuremath{\Phi}) is calculated for a one-dimensional copper-oxide model defined on a ring of finite length L, threaded by an external flux \ensuremath{\Phi}. It includes on-site and nearest-neighbor intersite Coulomb repulsion V, as well as a nonzero bare ``oxide'' gap ${\mathrm{\ensuremath{\Delta}}}_{0}$ between the orbitals in the unit cell. The correlation exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ of the corresponding low-energy Hamiltonian shows that singlet (extended s-wave) superconductivity has the most rapidly diverging susceptibility as T\ensuremath{\rightarrow}0 (${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1). This superconducting phase is located close to a phase-separation instability of the model, indicated by ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\rightarrow}\ensuremath{\infty}. Longer range of the Coulomb interaction tends to frustrate phase separation, enhances the range of V for which ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1, and slightly broadens the regime of V where 1${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\infty}.
The phase diagram of the copper-oxide chain as a function of density and the nearest-neighbour Coulomb interaction, V , is determined. Phase separation takes place above a critical value of V when the Cu 2+ → Cu + valence fluctuations dominate. In the proximity of the phase separation boundary the superconducting correlations are the most divergent. We identify the parameter regions where the Luttinger-liquid theory applies and calculate the contours of the charge-charge correlation exponent K ρ . We show that anomalous flux quantization occurs as K ρ diverges. At n = 1, for V > t , a gap opens in the spectrum and the ground state is a charge density wave.