Flat bands with non-trivial topology in three dimensions

Abstract

We construct a simple model for electrons in a three-dimensional crystal where a combination of short-range hopping and spin-orbit coupling results in nearly flat bands characterized by a non-trivial Z2 topological index. The flat band is separated from other bands by a bandgap much larger than the bandwidth. We discuss the fate of the many-body ground state of electrons in the flat band in the presence of repulsive interactions at partial filling and conjecture that it may become a three-dimensional fractional topological insulator if conventional magnetic instabilities can be avoided.

5 pages, 3 figures; references updated, minor changes to improve clarity of text, version to appear in PRB/RC

References in corpus (12)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Wannier representation of Z_2 topological insulators
• Topological Insulators on the Lieb and Perovskite Lattices
• Spin Hall effects for cold atoms in a light induced gauge potential
• Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
• Engineering artificial graphene in a two-dimensional electron gas
• Fractional topological insulators in three dimensions
• Topological Insulators and Metals in Atomic Optical Lattices

Cited by in corpus (31)

• Artificial flat band systems: from lattice models to experiments
• Topological Flat Band Models and Fractional Chern Insulators
• Exotic electronic states in the world of flat bands: from theory to material
• Towards Three-Dimensional Weyl-SurfaceSemimetals in Graphene Networks
• Detangling Flat Bands into Fano Lattices
• Classification of flat bands according to the band-crossing singularity of Bloch wave functions
• Massive symmetry breaking in LaAlO${}_3$/SrTiO${}_3$(111) quantum wells: a three-orbital, strongly correlated generalization of graphene
• Machine Learning Topological Phases with a Solid-state Quantum Simulator
• Flat band separation and robust spin-Berry curvature in bilayer kagome metals
• Flat bands and nontrivial topological properties in an extended Lieb lattice
• Fractional topological phase in one-dimensional flatbands with nontrivial topology
• General construction of flat bands with and without band crossings based on wave function singularity
• Giant Anomalous Hall Effect due to Double-Degenerate Quasi Flat Bands
• Flat Bands and Ferrimagnetic Order in Electronically Correlated Dice-Lattice Ribbons
• Disorder-induced topological phase transitions on Lieb lattices
• Flat bands with band crossings enforced by symmetry representation
• Edge Excitations in Fractional Chern Insulators
• Instabilities of a birefringent semi-metal
• Probing fractional topological insulators with magnetic edge perturbations
• Isolated flat bands in an interlocking-circles lattice
• Highly degenerate photonic flat bands arising from complete graph configurations
• Topological flat bands in optical checkerboard-like lattices
• Hard-core bosons in one-dimensional interacting topological bands
• Periodic and aperiodic dynamics of flat bands in diamond-octagon lattice
• Lieb's Theorem and Maximum Entropy Condensates
• Magnetization-Induced Phase Transitions on the surface of 3D Topological Insulators
• Self-organized critical behavior and marginality in Ising spin glasses
• Emergence of asymmetric fermionic order in interacting birefringent fermions
• Unconventional superconductivity in Sc${}_2$Ir${}_{4-x}$Si${}_x$ by spin-orbit coupling driven flat band
• Flat Bands in Three-dimensional Lattice Models with Non-trivial Hopf Index
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry