Fragile topology in line-graph lattices with two, three, or four gapped flat bands
arXiv:2010.11953 · doi:10.1103/PhysRevResearch.2.043414
Abstract
The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively. Line-graph lattices are a perfect example of both of these features: their lowest energy bands are perfectly flat, and here we develop a formalism to connect some of their geometric properties with the presence or absence of fragile topology in their flat bands. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits.
8+25 pages, 3+19 figures, 2+3 tables
References in corpus (10)
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
- Classification of topological insulators and superconductors in three spatial dimensions
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Double crystallographic groups and their representations on the Bilbao Crystallographic Server
- Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
- Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
- Graph Theory Data for Topological Quantum Chemistry
Cited by in corpus (21)
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- Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
- Flat bands with band crossings enforced by symmetry representation
- Non-Compact Atomic Insulators
- Isolated flat bands in 2D lattices based on a novel path-exchange symmetry
- Line-graph-lattice crystal structures of stoichiometric materials
- Dynamical Fragile Topology in Floquet Crystals
- Catalogue of Flat-Band Stoichiometric Materials
- Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
- Hund's coupling-assisted ferromagnetic percolation transition in a multiorbital flat band
- Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles
- Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence
- Flat Bands Arising from Spin-Orbit Assisted Orbital Frustration
- Dynamics of one-dimensional spin models under the line-graph operator
- Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
- Interorbital Antisymmetric Hopping Generated Flat Bands on Kagome and Pyrochlore Lattices
- Flat bands and band touching from real-space topology in hyperbolic lattices
- Symmetry-Based Real-Space Framework for Realizing Flat Bands and Unveiling Nodal-Line Touchings