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Physical review. B, Condensed matter

Superconducting instability of the resonating-valence-bond state

V. N. Muthukumar

Published Sep 1, 1992• 6 citations
Publisher

Abstract

Assuming the low-energy excitations in the Cu-O planes to be spin-charge decoupled, we show explicitly that an interlayer coupling gives rise to processes that involve hopping of singlet bonds between adjacent layers, if the spinons are paired. On tracing out the spinons, we obtain an effective Hamiltonian for the holons. This turns out to be the model for superconducting holons proposed earlier by Wheatley, Hsu, and Anderson.

DOI
10.1103/physrevb.46.5769

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Assuming the low-energy excitations in the Cu-O planes to be spin-charge decoupled, we show explicitly that an interlayer coupling gives rise to processes that involve hopping of singlet bonds between adjacent layers, if the spinons are paired. On tracing out the spinons, we obtain an effective Hamiltonian for the holons. This turns out to be the model for superconducting holons proposed earlier by Wheatley, Hsu, and Anderson.
We study the effective interaction between fermionic holons mediated by bosonic spinons in stacked layers described by the t-J model with a hopping coupling between the layers. This interaction is provided by the holon-spinon interaction beyond mean-field theory. The effective four-holon interaction drives (1) pure in-plane holon pairing; (2) holon pairing in one plane, provided that there is pairing in the other; and (3) interlayer holon pairing. The latter pairing does not lead to physical interlayer hole pairing. We discuss the influence of the Coulomb repulsion between the holons on the pairing picture that we have obtained.
A spin-charge binding mechanism is analyzed using the Schwinger boson representation of the two-dimensional $t\ensuremath{-}J$ model. In the normal state spinons are paired into singlets which evolve out of the antiferromagnetic phase at half-filling. The singlets induce, via the hopping term, a pairing of holons and bind with the latter. The ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry of the order parameter and the shape of the Tc{T}_{c}Tc​ vs doping curve, observed in cuprate superconductors, emerge naturally as a consequence of the symmetry of the spinon pairs, thus connecting superconductivity with quantum spin fluctuations in the insulator.
A Hamiltonian for the motion of oxygen holes strongly coupled to the Cu spins in a one-dimensional (1D) Cu-O lattice is solved exactly for all dopings. This Hamiltonian retains the dominant O-hole hopping term, that is, spin-exchange hopping of the hole spin with the intervening Cu spin and neglects the weaker non-spin-exchange hopping term. The excitations naturally separate into two independent quasiparticles: spinons and holons. It is this Hamiltonian that should be taken as the correct zeroth-order Hamiltonian from which perturbation theory should be applied. We show that the spinon spectrum is the spectrum of the 1D antiferromagnet incommensurate with the Cu lattice and the holons are spinless noninteracting fermions in a cosine band. The Cu-Cu spin correlation in the ground state increases linearly with doping from antiferromagnetic (-0.443) at x=0 to ferromagnetic (\ensuremath{\approxeq}0.19) at x=1.
Using continuity, we derive a renormalized Hamiltonian from the parent $t\text{\ensuremath{-}}J$ model to describe the properties of underdoped cuprates. The theory is constrained to agree with the behavior at half filling, which is well described by the Arovas-Auerbach valence bond state in which bosonic spinons are paired into singlets. Spinon states evolve continuously into the doped region preserving their symmetry. We assume that moving holes rapidly destroy magnetic order, which leads to a gap in the spinon spectrum and strongly renormalizes the theory. The spin gap leads to two different types hopping terms for renormalized holes. In one, a fermionic holon hops within the same sublattice accompanied by a singlet backflow, giving rise to a non-Fermi-liquid normal state with novel properties. Spinon singlets condense below a pseudogap temperature ${T}^{\ensuremath{\ast}}$ (<<< spin gap temperature T0{T}^{0}T0), which allows holons to propagate coherently, forming a spinless Fermi liquid, but without an observable holon Fermi surface. Above ${T}^{\ensuremath{\ast}}$, holons are localized. This is the so-called strange metal phase, which is actually a new type of insulator since its resistivity would be infinite at T=0T=0T=0. In the second term a pair of holons belonging to opposite sublattices hop, accompanied by a singlet backflow. In the presence of the singlet condensate holon pairs condense, leading to ddd-wave superconductivity; the symmetry is primarily determined by the symmetry of the valence bond state at half filling. The metal and the superconductor preserve the two-sublattice character of the valence bond state. A careful examination of the nuclear magnetic resonance, tunneling, and transport data shows that the predictions of the theory is consistent with experimental results. Remarkably, the existence of the spin gap provides a natural explanation for the phenomenon of two dimensionality of the normal state in the presence of interplane hopping. The marked asymmetry between hole-doped and electron-doped cuprates is also easily explained.