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arXiv:cond-mat/0208017 · Physical review. B, Condensed matter

Quasiparticles as composite objects in the resonating valence bond superconductor

Yi Zhou, V. N. Muthukumar, Zheng-Yu Weng

Published Feb 28, 2003• 14 citations
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Abstract

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.

DOI
10.1103/physrevb.67.064512

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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−Jt\ensuremath{-}Jt\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.
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.
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.
We show that the resonating valence bond (RVB) state of the t-J Hamiltonian can be described within an effective boson-fermion model. We derive a boson-fermion Hamiltonian which describes the lowest order coupling between holons and spinon waves. The RVB order parameter determines a hybridization between the both types of excitations. The effective Hamiltonian is investigated within the lowest order self-consistent conserving diagrammatic approximation. We compare our approach with the phenomenological boson--fermion model (BFM) that is believed to describe the pseudogap phase.
We construct a family of simple fermionic projected entangled pair states (fPEPS) on the square lattice with bond dimension D=3D=3D=3 which are exactly hole-doped resonating valence bond (RVB) wave functions with short-range singlet bonds. Under doping the insulating RVB spin liquid evolves immediately into a superconductor with mixed d+isd+isd+is pairing symmetry whose pair amplitude grows as the square root of the doping. The relative weight between sss-wave and ddd-wave components can be controlled by a single variational parameter ccc. We optimize our ansatz with respect to ccc for the frustrated $t\text{\ensuremath{-}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ model (including both nearest and next-nearest neighbor antiferromagnetic interactions J1{J}_{1}J1​ and J2{J}_{2}J2​, respectively) for ${J}_{2}\ensuremath{\simeq}{J}_{1}/2$ and obtain an energy very close to the infinite-PEPS state (using full update optimization and same bond dimension). The orbital symmetry of the optimized RVB superconductor has predominant ddd-wave character, although we argue a residual (complex sss-wave) time reversal symmetry breaking component should always be present. Connections of the results to the physics of superconducting cuprates and pnictides are outlined.
We show that, in the presence of Coulomb interactions, the charge of a quasiparticle in a fully gapped superconductor is a sharp quantum observable. It follows that the familiar Bogoliubov quasiparticles are neutral, spin-1/2 fermions. Since the current-carrying collective modes are spinless, charge and spin are carried by separate excitations in a superconductor. The quantum numbers of these quasiparticles are identical to those of a spinon in a ``resonating-valence-bond'' (RVB) superconductor. This supports the notion that a RVB superconductor is simply a strong-coupling version of a BCS superconductor. We describe an experiment that would directly verify the separation of charge and spin in a bulk superconductor.
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.