Fragile topology in line-graph lattices with two, three, or four gapped flat bands

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.

arXiv comment8+25 pages, 3+19 figures, 2+3 tables

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Cited by in corpus (21)

• Geometric characterization of anomalous Landau levels of isolated flat bands
• General construction of flat bands with and without band crossings based on wave function singularity
• Orbital Design of Flat Bands in Non-Line-Graph Lattices via Line-Graph Wavefunctions
• Symmetries as the guiding principle for flattening bands of Dirac fermions
• 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
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• 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