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Physical Review Letters

Effect of interplane coupling on anyon superconductivity

H. A. Fertig, Song He, S. Das Sarma

Published Apr 27, 1992• 3 citations
Publisher

Abstract

We consider the effect of interplane coupling J' on a pair of layers in the Kalmeyer-Laughlin model of anyon superconductivity. We show by exact diagonalization of an effective continuum model that this coupling has little effect on the chiral-spin-liquid ground state for small J'. For J' larger than twice the gap, one sees a transition away from the chiral spin liquid. We argue that the J' term should introduce short-range attractive interactions between holons in different layers. A model of anyons with such an interaction yields a phase diagram in qualitative agreement with what one expects when working directly with the spin system.

DOI
10.1103/physrevlett.68.2676

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We consider the effect of interplane coupling J' on a pair of layers in the Kalmeyer-Laughlin model of anyon superconductivity. We show by exact diagonalization of an effective continuum model that this coupling has little effect on the chiral-spin-liquid ground state for small J'. For J' larger than twice the gap, one sees a transition away from the chiral spin liquid. We argue that the J' term should introduce short-range attractive interactions between holons in different layers. A model of anyons with such an interaction yields a phase diagram in qualitative agreement with what one expects when working directly with the spin system.
We consider the effect of interplane coupling on the energetics of the relative sign of statistics of anyons in adjacent planes. We offer qualitative arguments as well as numerical results which support the idea that opposing chirality (i.e., ``antiferromagnetic'' order of the statistics) is favored over a wide range of interplane coupling V--including both attractive and repulsive interactions between planes. We argue that our results apply to the normal (nonsuperfluid) phase in the thermodynamic limit.
We present a multiplane model for the anyon problem. Anyons on different planes are coupled via a Coulomb–type interaction. We solve exactly finite clusters and show that the "antiferromagnetic" order of the chirality is favored for both attractive and repulsive interplane coupling. We also discuss a simple model that can be treated analytically and that has the same qualitative behavior as the exact results. Our results apply to the low density limit, in which finite currents exist in each plane. These currents also occur in the high temperature (nonsuperfluid) phase of the anyon system, and so our results should apply also to that regime.
A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon inter-layer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping δcδ_cδc​ due to the formation of excitons. A spin liquid insulator (SLI) phase is thus realized without the lattice frustration. The critical value δcδ_{c}δc​ sensitively depends on the inter-layer interaction strength. In the tJtJtJ model description of each layer with the d-wave pairing, δcδ_{c}δc​ marks the crossover between SLI and d-wave superconductor. The SLI phase, despite being non-superconducting and charge-gapped, still shows electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the tJtJtJ model introduces magnetically ordered phases at low doping and pushes the spin liquid phase to a larger inter-layer interaction strength and higher doping concentrations.
A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon interlayer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping ${\ensuremath{\delta}}_{c}$ due to the formation of excitons. A spin-liquid-insulator (SLI) phase is thus realized without the lattice frustration. The critical value ${\ensuremath{\delta}}_{c}$ sensitively depends on the interlayer interaction strength. In the $t\text{\ensuremath{-}}J$ model description of each layer with the ddd-wave pairing, ${\ensuremath{\delta}}_{c}$ marks the crossover between SLI and ddd-wave superconductor. The SLI phase, despite being nonsuperconducting and charge gapped, still shows an electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the $t\text{\ensuremath{-}}J$ model introduces magnetically ordered phases at low doping and pushes the spin-liquid phase to a larger interlayer interaction strength and higher doping concentrations.
We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground-state degeneracy on the torus signaling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field-theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.
We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground state degeneracy on the torus signalling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.