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arXiv:supr-con/9505001 · Physical review. B, Condensed matter

Superconductivity from correlated hopping

C. D. Batista, F. Lema, Armando A. Aligia

Published Sep 1, 1995• 11 citations
arXivHTMLPDF

Abstract

We consider a chain described by a next-nearest-neighbor hopping combined with a nearest-neighbor spin flip. In two dimensions this three-body term arises from a mapping of the three-band Hubbard model for ${\mathrm{CuO}}_{2}$ planes to a generalized t-J model and for large O-O hopping favors resonance-valence-bond superconductivity of predominantly d-wave symmetry. Solving the ground-state and low-energy excitations by analytical and numerical methods we find that the chain is a Luther-Emery liquid with correlation exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$=(2-n${)}^{2}$/2, where n is the particle density.

DOI
10.1103/physrevb.52.6223

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Correlated-electron theories of superconductivity in layered cuprates often start from the premise of a gapped spin-liquid phase proximate to the superconducting state. This assumption is justified based on analytical and numerical demonstrations of a superconducting Luther-Emery phase in the doped 2-leg one-band Hubbard ladder, and the perceived analogy between coupled ladders and the two-dimensional ${\mathrm{CuO}}_{2}$ layer. We demonstrate from accurate density matrix renormalization group studies the absence of the superconducting Luther-Emery phase in the doped 2-leg three-band ladder consisting of both copper and oxygen, even as the spin gap is large in the undoped three-band ladder. For realistic oxygen-oxygen hopping and Hubbard repulsion on the oxygen atoms, density-density rather than pairing correlations are dominant at long range. This result is equally valid whether or not the oxygens outside the ladder proper, over and above the rung and leg oxygens, are included in the computation. These results demonstrate the critical importance of oxygen orbitals, and raise disturbing questions about the applicability of many of the existing correlated-electron theories of superconductivity.

arXiv:2010.10609•Physical review. B./Physical review. B•Sep 13, 2021•9 citations
We consider a chain described by a next-nearest-neighbor hopping combined with a nearest-neighbor spin flip. In two dimensions this three-body term arises from a mapping of the three-band Hubbard model for CuO2{\mathrm{CuO}}_{2}CuO2​ planes to a generalized t-J model and for large O-O hopping favors resonance-valence-bond superconductivity of predominantly d-wave symmetry. Solving the ground-state and low-energy excitations by analytical and numerical methods we find that the chain is a Luther-Emery liquid with correlation exponent K\ensuremathρ{\mathit{K}}_{\mathrm{\ensuremath{\rho}}}K\ensuremathρ​=(2-n)2{)}^{2})2/2, where n is the particle density.
A lightly doped single-band Hubbard model on a two leg ladder exhibits a Luther-Emery phase, while the three-band Hubbard ladder behaves as a Luttinger liquid upon hole doping. In order to understand this discrepancy, we present a systematic density-matrix renormalization group study of the three-band Hubbard model on two-leg cylinders with further-neighbor particle hoppings. The inclusion of the longer-range hopping is motivated by the studies of the single-band Hubbard model in which the further-neighbor hopping terms are suggested to be crucial for the unconventional superconductivity. When the longer-range hopping parameters are small, the ground state is a Luttinger liquid having mutually commensurate superconducting, charge and spin density wave correlations. Increasing the longer-range hopping drives a transition into a Luther-Emery phase with quasi-long ranged superconducting and charge orders but short-ranged spin-spin correlations. By down-folding the three-band Hubbard model into an effective ttt-t′t't′-JJJ-J′J'J′ model, we find that in the Luther-Emery phase, both the nearest and second neighbor kinetic energies are enhanced due to an effective increase of copper-oxygen hybridization. Amplifying inter-cell oxygen orbital hopping mirrors the benefits of reducing the charge transfer energy, causing doped holes to favor oxygen orbitals and strengthening superconducting pairing.
A lightly doped single-band Hubbard model on a two-leg ladder exhibits a Luther-Emery phase, whereas the three-band Hubbard ladder behaves as a Luttinger liquid upon hole doping. To understand this discrepancy, we present a systematic density-matrix renormalization group study of the three-band Hubbard model on two-leg cylinders with further-neighbor particle hoppings. The inclusion of the longer-range hopping is motivated by the studies of the single-band Hubbard model in which the further-neighbor hopping terms are suggested to be crucial for the unconventional superconductivity. When the longer-range hopping parameters are small, the ground state is a Luttinger liquid having mutually commensurate superconducting, charge, and spin density wave correlations. Increasing the longer-range hopping drives a transition into a Luther-Emery phase with quasi-long-ranged superconducting and charge orders but short-ranged spin-spin correlations. By down-folding the three-band Hubbard model into an effective $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J\text{\ensuremath{-}}{J}^{\ensuremath{'}}$ model, we find that in the Luther-Emery phase, both the nearest- and second-neighbor kinetic energies are enhanced due to an effective increase of copper-oxygen hybridization. Amplifying intercell oxygen orbital hopping mirrors the benefits of reducing the charge transfer energy, causing doped holes to favor oxygen orbitals and strengthening superconducting pairing.
We investigate the ground-state properties of a correlated model for the double-chain structure in cuprates. We consider the ttt-JJJ model, in which the nearest-neighbor spin interaction J1J_1J1​ is smaller than the next-nearest-neighbor interaction J2J_2J2​ corresponding to the CuO double-chain structure. We vary J1J_1J1​ from antiferromagnetic to ferromagnetic values and calculate the correlation functions including the superconducting pair correlation function. Employing the density-matrix renormalization group method, we show that the ground state for antiferromagnetic J1J_1J1​ exhibits the hallmarks of the Luther-Emery liquid phase, in which the spin-singlet pair and charge-density-wave correlations exhibit power-law decays against distance, and the spin correlation function decays exponentially. Its signatures are gradually dismissed as J1J_1J1​ approaches the ferromagnetic regime. Our findings suggest that the antiferromagnetic double-chain structure without ferromagnetic bonds is favorable for superconductivity.
We evaluate numerically several superconducting correlation functions in a generalized t−Jt-Jt−J model derived for hole-doped CuO2_22​ planes. The model includes a three-site term t′′t''t′′ similar to that obtained in the large UUU limit of the Hubbard model but of opposite sign for realistic O-O hopping. For realistic parameters we obtain strong evidence of superconductivity of predominantly dx2−y2d_{x^2-y^2}dx2−y2​ character. The ground state has a large overlap with a very simple resonating-valence-bond wave function with off-diagonal long-range order. This function reproduces the main features of the magnetic and superconducting correlation functions.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (JJJ) and correlated hopping (KKK) interaction. Detailed numerical analysis of sss-, ppp-, and ddd-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (ttt) and next-nearest- (t2{t}_{2}t2​) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the ddd-wave and the extended sss-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the t2t\frac{{t}_{2}}{t}tt2​​ ratio, giving in particular for t2=0{t}_{2}=0t2​=0 sss-wave (ddd-wave) pairing as most favorable in the low (high) density limit, but increasing t2{t}_{2}t2​ can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects sss-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.
Correlated-electron theories of superconductivity in layered cuprates often start from the premise of a gapped spin-liquid phase proximate to the superconducting state. This assumption is justified based on analytical and numerical demonstrations of a superconducting Luther-Emery phase in the doped 2-leg one-band Hubbard ladder, and the perceived analogy between coupled ladders and the two-dimensional CuO2{\mathrm{CuO}}_{2}CuO2​ layer. We demonstrate from accurate density matrix renormalization group studies the absence of the superconducting Luther-Emery phase in the doped 2-leg three-band ladder consisting of both copper and oxygen, even as the spin gap is large in the undoped three-band ladder. For realistic oxygen-oxygen hopping and Hubbard repulsion on the oxygen atoms, density-density rather than pairing correlations are dominant at long range. This result is equally valid whether or not the oxygens outside the ladder proper, over and above the rung and leg oxygens, are included in the computation. These results demonstrate the critical importance of oxygen orbitals, and raise disturbing questions about the applicability of many of the existing correlated-electron theories of superconductivity.