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Physical Review Letters

Flux quantization and pairing in one-dimensional copper-oxide models

Asle Sudbø, C. M. Varma, Thierry Giamarchi, Ellen B. Stechel, Richard T. Scalettar

Published Feb 15, 1993• 47 citations
Publisher

Abstract

We obtain the ground-state energy ${\mathit{E}}_{0}$(\ensuremath{\Phi}) exactly as a function of flux \ensuremath{\Phi} in a one-dimensional ``copper-oxide model'' on rings of finite circumference L, including on-site interactions and a nearest-neighbor interaction V. For V of the order of the charge-transfer gap or larger, the model extrapolated to large L exhibits flux quantization with charge 2e, and a slow algebraic decay of the singlet superconducting correlation function on oxygen sites. The extrapolated superfluid stiffness appears, however, finite only for not too large V. These results suggest a superconductive state at V of order the charge-transfer gap of the model, but a paired and phase-separated state at larger V.

DOI
10.1103/physrevlett.70.978

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•Jan 1, 1994•3 citations
We obtain the ground-state energy E0{\mathit{E}}_{0}E0​(\ensuremath{\Phi}) exactly as a function of flux \ensuremath{\Phi} in a one-dimensional ``copper-oxide model'' on rings of finite circumference L, including on-site interactions and a nearest-neighbor interaction V. For V of the order of the charge-transfer gap or larger, the model extrapolated to large L exhibits flux quantization with charge 2e, and a slow algebraic decay of the singlet superconducting correlation function on oxygen sites. The extrapolated superfluid stiffness appears, however, finite only for not too large V. These results suggest a superconductive state at V of order the charge-transfer gap of the model, but a paired and phase-separated state at larger V.
A calculation of the ground state energy E0(Φ) as a function of flux Φ in a one-dimensional `copper-oxide model' on rings of finite circumference L, including on-site interactions, and a nearest neighbor interaction V, is presented. For V of the order of the charge-transfer gap or larger, the model extrapolated to large L exhibits flux-quantization with charge 2e. The extrapolated superfluid stiffness appears, however, finite only for not too large V. These results suggest a superconductive state at V of order the charge-transfer gap of the model, but a paired and phase-separated state at larger V.
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 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.
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.
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.
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 Kρ. We show that anomalous flux quantization occurs as Kρ diverges. At n = 1, for V> t, a gap opens in the spectrum and the ground state is a charge-density wave.