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arXiv:cond-mat/0002233 · Physical Review Letters

Luther-Emery Stripes, Resonating Valence Bond Spin Liquid Background, and High Tc Superconductivity

Wenjun Zheng

Published Oct 25, 1999• 5 citations
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Abstract

The stripe phase in high ${T}_{c}$ cuprates is modeled as a single stripe coupled to the resonating valence bond (RVB) spin liquid background by the single particle hopping process. In the normal state, the strong pairing correlation inherent in a RVB state is thus transferred into the Luttinger stripe and drives it toward spin-gap formation described by the Luther-Emery model. The establishment of global phase coherence in the superconducting state contributes to a more relevant coupling to Luther-Emery stripe and leads to gap opening in both spin and charge sectors. Physical consequences of the present picture are discussed.

DOI
10.1103/physrevlett.83.3534

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The stripe phase in high Tc{T}_{c}Tc​ cuprates is modeled as a single stripe coupled to the resonating valence bond (RVB) spin liquid background by the single particle hopping process. In the normal state, the strong pairing correlation inherent in a RVB state is thus transferred into the Luttinger stripe and drives it toward spin-gap formation described by the Luther-Emery model. The establishment of global phase coherence in the superconducting state contributes to a more relevant coupling to Luther-Emery stripe and leads to gap opening in both spin and charge sectors. Physical consequences of the present picture are discussed.
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.
Correlated-electron theories of superconductivity in cuprates often start from the premise of a gapped spin-liquid phase proximate to the superconducting state. This assumption is based on, (i) demonstrations of a Luther-Emery phase with dominant superconducting correlations in the doped 2-leg one-band Hubbard ladder, and (ii) the perceived analogy between coupled ladders and the square lattice. We demonstrate from accurate density matrix renormalization group calculations the absence of the Luther-Emery phase in the doped 2-leg three-band ladder consisting of both copper and oxygen. For realistic oxygen-oxygen hopping and Hubbard repulsion on the oxygen atoms, the decay of the superconducting pair correlation with distance is almost indistinguishable from that of free fermions. Our results caste severe doubts on many of the existing correlated-electron theories of superconductivity.
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.
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 ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$=(2-n)2{)}^{2})2/2, where n is the particle density.
There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around xc{x}_{c}xc​, the end point of the superconducting dome on the overdoped side, where the cuprate is believed to be well described by the Fermi-liquid theory. This is the most evident in the observed ${\ensuremath{\rho}}_{s}(0)\ensuremath{-}{T}_{c}$ scaling and the large amount of uncondensed optical spectral weight at low energy. The second puzzle concerns the remarkable robustness of the ddd-wave pairing against the inevitable disorder effect in such a doped system, which is also totally unexpected from the conventional BCS picture. Here we show that these two puzzles are deeply connected to the origin of a third puzzle about the cuprate superconductors, namely, the mysterious quantum critical behavior observed around x∗{x}^{*}x∗, the so called pseudogap end point. Through a systematic variational Monte Carlo (VMC) study of the disordered 2D $t\ensuremath{-}J$ model from the resonating valence bond (RVB) perspective, we find that the ddd-wave pairing in this model is remarkably more robust against the disorder effect than that in a conventional ddd-wave BCS superconductor. We find that such remarkable robustness can be attributed to the spin-charge separation mechanism in the RVB picture, through which the ddd-wave RVB pairing of the charge-neutral spinons becomes essentially immune to the disorder potential except for the secondary effect related to the modulation of the local doping level by the disorder. We propose that there exists a Mott transition at x∗{x}^{*}x∗, where the RVB pairing in the underdoped regime is transmuted into the increasingly more BCS-like pairing for x>x∗x>{x}^{*}x>x∗, whose increasing fragility against the disorder effect leads to the non-BCS behavior and the ultimate suppression of superconductivity around xc{x}_{c}xc​.