Topological insulators and fractional quantum Hall effect on the ruby lattice

Abstract

We study a tight-binding model on the two-dimensional ruby lattice. This lattice supports several types of first and second neighbor spin-dependent hopping parameters in an $s$-band model that preserves time-reversal symmetry. We discuss the phase diagram of this model for various values of the hopping parameters and filling fractions, and note an interesting competition between spin-orbit terms that individually would drive the system to a $Z_2$ topological insulating phase. We also discuss a closely related spin-polarized model with only first and second neighbor hoppings and show that extremely flat bands with finite Chern numbers result, with a ratio of the band gap to the band width approximately 70. Such flat bands are an ideal platform to realize a fractional quantum Hall effect at appropriate filling fractions. The ruby lattice can be possibly engineered in optical lattices, and may open the door to studies of transitions between quantum spin liquids, topological insulators, and integer and fractional quantum Hall states.

9 pages, 8 figures, updated figures, updated references, updated acknowledgement, some details in calculation added

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• Prediction of Toric Code Topological Order from Rydberg Blockade
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
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• Topological flat band models with arbitrary Chern numbers
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Topological insulators from complex orbital order in transition-metal oxides heterostructures
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• Fractional Chern Insulators and the W-Infinity Algebra
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• Flat bands with higher Chern number in pyrochlore slabs
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• Hierarchy of fractional Chern insulators and competing compressible states
• Band structure engineering of ideal fractional Chern insulators
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Fractional quantum-Hall liquid spontaneously generated by strongly correlated t_2g electrons
• Strongly interacting Majorana fermions
• Quantum s = 1/2 Antiferromagnets on Archimedean Lattices: The Route from Semiclassical Magnetic Order to Nonmagnetic Quantum States
• Fractional Chern Insulators beyond Laughlin states
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• From Fractional Chern Insulators to a Fractional Quantum Spin Hall Effect
• Topological phases in layered pyrochlore oxide thin films along the [111] direction
• Symmetry protected fractional Chern insulators and fractional topological insulators
• Flat bands with non-trivial topology in three dimensions
• Strain induced topological phase transitions in monolayer honeycomb structures of group-V binary compounds
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Quasicrystalline Chern Insulators
• Lattice construction of pseudopotential Hamiltonians for Fractional Chern Insulators
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• Fractional topological phase in one-dimensional flatbands with nontrivial topology
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Bulk-edge correspondence in fractional Chern insulators
• Flat Bands and Ferrimagnetic Order in Electronically Correlated Dice-Lattice Ribbons
• Topological Insulators and Quantum Spin Liquids
• Characterization of quasiholes in fractional Chern insulators
• Antiferromagnetic topological insulators in cold atomic gases
• The fundamental differences between Quantum Spin Hall edge-states at zig-zag and armchair terminations of honeycomb and ruby nets
• Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature
• Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
• Edge Excitations in Fractional Chern Insulators
• Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
• Topological states in a dimerized system with staggered magnetic fluxes
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• Tuning the topological insulator states of artificial graphene
• Hyperbolic Fractional Chern insulators
• Hard-core bosons in one-dimensional interacting topological bands
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• Flat bands and $Z_2$ topological phases in a non-Abelian kagome lattice
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice
• Walking on Archimedean Lattices: Insights from Bloch Band Theory
• Chiral spin liquid from magnetic Wannier states
• Coexistence of flat bands and Dirac bands in a carbon-Kagome-lattice family
• Exact Mappings in Condensed Matter Physics