Fractional topological liquids with time-reversal symmetry and their lattice realization

Abstract

We present a class of time-reversal-symmetric fractional topological liquid states in two dimensions that support fractionalized excitations. These are incompressible liquids made of electrons, for which the charge Hall conductance vanishes and the spin Hall conductance needs not be quantized. We then analyze the stability of edge states in these two-dimensional topological fluids against localization by disorder. We find a Z_2 stability criterion for whether or not there exists a Kramers pair of edge modes that is robust against disorder. We also introduce an interacting electronic two-dimensional lattice model based on partially filled flattened bands of a Z_2 topological band insulator, which we study using numerical exact diagonalization. We show evidence for instances of the fractional topological liquid phase as well as for a time-reversal symmetry broken phase with a quantized (charge) Hall conductance in the phase diagram for this model.

14 pages, 2 figures

References in corpus (17)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Topological Mott Insulators
• Fractional quantum Hall effect in the absence of Landau levels
• Electron fractionalization in two-dimensional graphenelike structures
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
• Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices
• Chiral Gauge Theory for Graphene
• Interaction effects and quantum phase transitions in topological insulators
• Electron fractionalization for two-dimensional Dirac fermions
• Irrational vs. rational charge and statistics in two-dimensional quantum systems
• Magnetic Response in Quantized Spin Hall Phase of Correlated Electrons

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• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
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• Fractional Topological Insulators -- a Pedagogical Review
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