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Physical Review Letters

Superconducting Ground State of Noninteracting Particles Obeying Fractional Statistics

R. B. Laughlin

Published Jun 20, 1988• 600 citations
Publisher

Abstract

In a previous paper, Kalmeyer and Laughlin argued that the elementary excitations of the original Anderson resonating-valence-bond model might obey fractional statistics. In this paper, it is shown that an ideal gas of such particles is a new kind of superconductor.
DOI
10.1103/physrevlett.60.2677

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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 have studied the ground-state (GS) properties of fractional-statistics particles (anyons) by exact numerical solution for small systems. We have seen in our results (depending on the choice of parameters for the Hamiltonian) the fractional-statistics analogs of a number of well-known ground states for conventional particles, including particularly the quantum Hall state (which we relate to the observed ‘hierarchy’ states), and a superconducting GS, the latter being formed (for half-statistics particles or semions) by pairing. We suggest possible experimental signatures for distinguishing semion from fermion superconductors. We also directly test the ‘mean-field theory’ of statistics against our exact results, and find it to treat GS properties well.