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Physica Scripta

A model for holon condensation in an RVB superconductor

E. J. Melé

Published Jan 1, 1989• 14 citations
Publisher

Abstract

A quasiparticle description of the hole doped "short range" RVB state is developed and it is applied to study the ground state properties of the interacting many holon fluid. The model is based on the conjecture that the elementary charged excitation of the RVB state, the holon, corresponds to an quantized vortex in a condensed quantum fluid of mobile singlets. The doped RVB state is described as a two component fluid of these quasiparticles with repulsive electrostatic interparticle interactions and an effective U(1) gauge field coupling the motion of these objects to the condensed particles of the parent RVB fluid. In this model for the doped state we find: (1) Quantum commensurability effects in the doped state, similar to those encountered in the fractional quantum Hall problem, lead to phase segregation of a doped state which corresponds to a 20% dilution of the doped antiferromagnet. (2) The ground state of the interacting holon fluid at this density is found to exhibit off diagonal long range order, describing a two-dimensional pairing condensation of the holons.

DOI
10.1088/0031-8949/1989/t27/013

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A systematic ``loop-gas'' formalism is developed for a general study of the resonance-valence-bond (RVB) states of a quantum antiferromagnet. At half-filling, we obtain analytic, parameter-free RVB amplitudes which reproduce virtually exact ground-state energy and spin excitation spectrum. A doped hole is then modeled by a holon-spinon pair moving on this optimized RVB background. Its energy is in excellent agreement with other estimates on the finite lattice for t/J\ensuremath{\le}1. Such a pair wave function shows a finite amplitude even at infinite separation. Spin-charge separation and vanishing quasiparticle spectral weight are discussed in this framework. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Jan 1, 1996•4 citations
A quasiparticle description of the hole doped "short range" RVB state is developed and it is applied to study the ground state properties of the interacting many holon fluid. The model is based on the conjecture that the elementary charged excitation of the RVB state, the holon, corresponds to an quantized vortex in a condensed quantum fluid of mobile singlets. The doped RVB state is described as a two component fluid of these quasiparticles with repulsive electrostatic interparticle interactions and an effective U(1) gauge field coupling the motion of these objects to the condensed particles of the parent RVB fluid. In this model for the doped state we find: (1) Quantum commensurability effects in the doped state, similar to those encountered in the fractional quantum Hall problem, lead to phase segregation of a doped state which corresponds to a 20% dilution of the doped antiferromagnet. (2) The ground state of the interacting holon fluid at this density is found to exhibit off diagonal long range order, describing a two-dimensional pairing condensation of the holons.
We present a formulation of the resonating-valence-bond theory of the large-UUU one-band Hubbard model in two dimensions, in which the correlated ground state of the system is represented as a fluid of mobile singlet bonds. We describe this fluid as a quantum fluid of interacting hardcore bosons, and a ground-state wave function for the interacting bosons is studied in which two-body correlations are introduced by applying techniques previously developed in Laughlin's theory of the fractional quantum Hall problem. The resulting many-particle state in this formulation exhibits an incipient momentum space condensation and a class of particlelike excitations in the form of quantized vortices which possess fractional particle number, and interesting dynamics. Application of this model to the doped state reveals a mechanism by which the electrostatic repulsive interactions between the charged quasiparticles in the doped fluid stabilize the resonating state relative to the doped N\'eel state at discrete well-correlated "commensurate" hole concentrations. A superconducting state in this doped fluid arises from a condensation which pairs the charged quasiparticles; it is identified as the most stable of a hierarchy of possible condensed quasiparticle states. The condensed state exhibits many properties associated with conventional superconductivity, including dissipationless flow of current, Meissner effect, and flux quantization in units of hc2e\frac{\mathrm{hc}}{2e}2ehc​.
We study the nature of the superconducting state, the origin of d-wave pairing, and elementary excitations of a resonating valence bond (RVB) superconductor. We show that the phase string formulation of the $t\ensuremath{-}J$ model leads to confinement of bare spinon and holon excitations in the superconducting state, though the vacuum is described by the RVB state. Nodal quasiparticles are obtained as composite excitations of spinon and holon excitations. The d-wave pairing symmetry is shown to arise from short-range antiferromagnetic correlations.
The RVB state is a singlet quantum liquid which can support periodic or fluid-like quantum circulation around the elementary plaquette in two dimensions. In the s + id phase there is a half flux quanta of circulation in every elementary plaquette. We show that the holons in the presence of this lattice of circulation have a two-valley structure, as opposed to "s"or "d" states, which have a single valley. Using an effective holon Hamiltonian, we study the mean-field properties of the two-valley holon condensate, and compare its energy with the single valley case. A transition from the "d" to the "s + id" state is predicted with increasing hole concentration for sufficiently large Hubbard U. Some speculations are offered about the general case of a fluid-like distribution of flux quanta.
We propose a class of ground states for doped Mott insulators in the electron second quantization representation. They are obtained from a bosonic resonating valence bond (RVB) theory of the $t\text{\penalty1000-\hskip0pt}J$ model. At half filling, the ground state describes spin correlations of the S=1∕2S=1∕2S=1∕2 Heisenberg model very accurately. Its spin degrees of freedom are characterized by RVB pairing of spins, the size of which decreases continuously as holes are doped into the system. Charge degrees of freedom emerge upon doping and are described by twisted holes in the RVB background. We show that the twisted holes exhibit an off diagonal long range order (ODLRO) in the pseudogap ground state, which has a finite pairing amplitude, but is short of phase coherence. Unpaired spins in such a pseudogap ground state behave as free vortices, preventing superconducting phase coherence. The existence of nodal quasiparticles is also ensured by such a hidden ODLRO in the ground state, which is non-Fermi liquidlike in the absence of superconducting phase coherence. Two distinct types of spin excitations can also be constructed. The superconducting instability of the pseudogap ground state is discussed and a ddd-wave superconducting ground state is obtained. This class of pseudogap and superconducting ground states unifies antiferromagnetism, pseudogap, superconductivity, and Mott physics into a new state of matter.
A d-wave superconducting ground state for a doped Mott insulator is obtained. It is distinguished from a Gutzwiller-projected Bardeen–Cooper–Schrieffer (BCS) superconductor by an explicit separation of Cooper pairing and resonating valence bond (RVB) pairing. Such a state satisfies the precise sign structure of the t–J model, just as a BCS state satisfies the Fermi–Dirac statistics. This new class of wavefunctions can be intrinsically characterized and effectively manipulated by electron fractionalization with neutral spinons and 'backflow' spinons forming a two-component RVB structure. While the former spinon is bosonic, originating from the superexchange correlation, the latter spinon is found to be fermionic, accompanying the hopping of bosonic holons. The low-lying emergent gauge fields associated with such a specific fractionalization are of mutual Chern–Simons type. Corresponding to this superconducting ground state, three types of elementary excitations are identified. Among them a Bogoliubov nodal quasiparticle is conventional, while the other two are neutral excitations of non-BCS type that play crucial roles in higher-energy/temperature regimes. Their unique experimental implications for the cuprates are briefly discussed.
A systematic ``loop-gas'' formalism is developed for a general study of the resonance-valence-bond (RVB) states of a quantum antiferromagnet. At half-filling, we obtain analytic, parameter-free RVB amplitudes which reproduce virtually exact ground-state energy and spin excitation spectrum. A doped hole is then modeled by a holon-spinon pair moving on this optimized RVB background. Its energy is in excellent agreement with other estimates on the finite lattice for t/J\ensuremath{\le}1. Such a pair wave function shows a finite amplitude even at infinite separation. Spin-charge separation and vanishing quasiparticle spectral weight are discussed in this framework. \textcopyright{} 1996 The American Physical Society.