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Journal of Physics and Chemistry of Solids

Theory of positron annihilation in the spinon-holon picture

S. E. Barnes

Published Jan 1, 1991• 2 citations
Publisher

Abstract

Discussed are the generic predictions of theories based upon the spinon-holon picture. In such theories there is a separation of the charge degrees of freedom associated with the holons and the spin degrees of freedom associated with the spinons. The nature of the spinon ground state, near to halt filling (one physical electron per site) is of key importance. There are two general classes of spinon ground states. One class consists of ground states which cause there to exist a fictitious magnetic flux, either time independent or fluctuating. Within the second class there exists a BCS pair amplitude. While, at half filling, these two types of pairing are equivalent, by virtue of an SU(2) symmetry, for a finite doping, the predictions for the momentum distribution are quite different. These generic issues are illustrated by simple model calculations.

DOI
10.1016/0022-3697(91)90136-n

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Discussed are the generic predictions of theories based upon the spinon-holon picture. In such theories there is a separation of the charge degrees of freedom associated with the holons and the spin degrees of freedom associated with the spinons. The nature of the spinon ground state, near to halt filling (one physical electron per site) is of key importance. There are two general classes of spinon ground states. One class consists of ground states which cause there to exist a fictitious magnetic flux, either time independent or fluctuating. Within the second class there exists a BCS pair amplitude. While, at half filling, these two types of pairing are equivalent, by virtue of an SU(2) symmetry, for a finite doping, the predictions for the momentum distribution are quite different. These generic issues are illustrated by simple model calculations.
In this paper, the authors discuss a class of quasi-one-dimensional models containing both spins and charge, which share the same generic solutions. In particular, they concentrate on a Heisenberg model of a topologically frustrated antiferromagnet, and a d-p model for oxygen hole hopping in a subgeometry of the copper-oxygen plane of the perovskite superconductors. The outstanding feature of these models lies in the simplicity of their solutions: their ground states are exact and contain uncorrelated, short-ranged singlet pairs. Excitations in these models fall into two distinct classes, namely, spin-1/2 chargeless domain-wall excitations or 'spinons', together with their conjugate excitations, which take the form of spin-1/2 chargeless 'antispinon' domain walls in the Heisenberg model, and spinless charge+e hole excitations or 'holons' in the d-p model. In the case of the Heisenberg model, the authors have successfully constructed a sufficiently simple representation for the 'spinon' excitation which allows them to calculate its dispersion using elementary methods. This is therefore a concrete example of a 'spinon' excitation for which explicit representation has been possible.
A fermion-spin transformation is used to implement the charge-spin separation, and is developed to study the low-dimensional t-J model. In this approach, the charge and spin degrees of freedom of the physical electron are separated, and the charge degree of freedom is represented by a spinless fermion while the spin degree of freedom is representd by a hard-core boson. The on-site local constraint for single occupancy is satisfied even in the mean-field approximation and the sum rule for the physical electron is obeyed. This approach can be applied to both one and two-dimensional systems. In the one-dimensional case, the spinon as well as the physical electron behave like Luttinger liquids. We have obtained a gapless charge and spin excitation spectrum, a good ground state energy, and a reasonable electron-momentum distribution within the mean-field approximation. The correct exponents of the correlation functions and momentum distribution are also obtained if the squeezing effect and rearrangement of the spin configurations are taken into account. In the two-dimensional case, within the mean-field approximation the magnetized flux state with a gap in the spinon spectrum has the lowest energy at half filling. The antiferromagnetic long-range order is destroyed by hole doping of the order \ensuremath{\sim}10-15 % for t/J=3-5 and a disordered flux state with gapless spinon spectrum becomes stable. The calculated specific heat is roughly consistent with observed results on copper oxide superconductors. The possible phase separation is also discussed at the mean-field level.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
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.