Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
arXiv:2307.01851 · doi:10.1103/PhysRevB.109.245402
Abstract
Chiral symmetry plays an indispensable role in topological classifications as well as in the understanding of the origin of bulk or boundary flat bands. The conventional definition of chiral symmetry refers to the existence of a constant unitary matrix anticommuting with the Hamiltonian. As a constant unitary matrix has constant eigenvectors, boundary flat bands enforced by chiral symmetry, which share the same eigenvectors with the chiral symmetry operator, are dictated to carry fixed (pseudo)spin polarizations and be featureless in quantum geometry. In this work, we generalize the chiral symmetry and introduce a concept termed sub-chiral symmetry. Unlike the conventional chiral symmetry operator defined as constant matrix, the sub-chiral symmetry operator depends on partial components of the momentum vector, so as its eigenvectors. We show that topological gapped or gapless systems without chiral symmetry but with sub-chiral symmetry can support boundary flat bands, which exhibit topological spin textures and quantized Berry phases. We expect that such intriguing boundary flat bands could give rise to a variety of exotic physics in the presence of interactions or disorders.
6+6 pages, 2 figures
References in corpus (66)
- The electronic properties of graphene
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Berry Phase Effects on Electronic Properties
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- Topological Photonics
- Classification of topological insulators and superconductors in three spatial dimensions
- Moire bands in twisted double-layer graphene
- Classification of topological quantum matter with symmetries
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Periodic table for topological insulators and superconductors
- Topological nodal semimetals
- Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Topological nodal line semimetals with and without spin-orbital coupling
- Dirac Line Nodes in Inversion Symmetric Crystals
- Topological Nodal Line Semimetal and Dirac Semimetal State in Antiperovskite CuPdN
- Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
- Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
- Topolectrical circuits
- Topological kagome magnets and superconductors
- Artificial flat band systems: from lattice models to experiments
- Topological Flat Band Models and Fractional Chern Insulators
- High-temperature surface superconductivity in topological flat-band systems
- Fractional Quantum Hall Physics in Topological Flat Bands
- Superfluidity and Quantum Geometry in Twisted Multilayer Systems
- Topology of Andreev Bound States with Flat Dispersion
- Nodal-link semimetals
- Flat bands in topological media
- Topological phases and surface flat bands in superconductors without inversion symmetry
- Kagome superconductors AVSb (A=K, Rb, Cs)
- Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
- Exotic electronic states in the world of flat bands: from theory to material
- Topological semimetals with double-helix nodal link
- Nodal-knot semimetals
- Compact localized states and flatband generators in one dimension
- Anomalous Andreev bound state in non-centrosymmetric superconductors
- Isolated Flat Bands and Spin-1 Conical Bands in Two-Dimensional Lattices
- Chiral Flat Bands: Existence, Engineering and Stability
- A simple method to construct Flat Band lattices
- Superconductivity from Flat Dispersion Designed in Doped Mott Insulators
- Crossed surface flat bands of Weyl semimetal superconductors
- Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
- Majorana Flat Bands and Uni-directional Majorana Edge States in Gapless Topological Superconductors
- Non-abelian gauge fields in circuit systems
- Flat bands in fractal-like geometry
- Screening 2D materials with topological flat bands
- Compact localized states and flat bands from local symmetry partitioning
- Universal flatband generator from compact localized states
- Flatband generator in two dimensions
- Realization of a Hopf insulator in circuit systems
- Flat bands with non-trivial topology in three dimensions
- Flat bands by latent symmetry
- Non-Abelian inverse Anderson transitions
- Edge-Ferromagnetism from Majorana Flat-Bands: Application to Split Tunneling-Conductance Peaks in the High-Tc Cuprates
- Majorana flat bands, chiral Majorana edge states, and unidirectional Majorana edge states in noncentrosymmetric superconductors
- Fragile topology in line-graph lattices with two, three, or four gapped flat bands
- General construction of flat bands with and without band crossings based on wave function singularity
- Majorana Flat Bands in s-Wave Gapless Topological Superconductors
- Perfect flat band with chirality and charge ordering out of strong spin-orbit interaction
- Molecular-orbital representation of generic flat-band models
- Observation of inverse Anderson transitions in Aharonov-Bohm topolectrical circuits
- Flat-band solutions in -dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem
- Majorana Doublets, Flat Bands, and Dirac Nodes in s-Wave Superfluids
- Methods for constructing parameter-dependent flat band lattices