Orbital Design of Flat Bands in Non-Line-Graph Lattices via Line-Graph Wavefunctions
arXiv:2104.14163 · doi:10.1103/PhysRevB.105.085128
Abstract
Line-graph (LG) lattices are known for having flat bands (FBs) from the destructive interference of Bloch wavefunctions encoded in pure lattice symmetry. Here, we develop a generic atomic/molecular orbital design principle for FBs in non-LG lattices. Based on linear-combination-of-atomic-orbital (LCAO) theory, we demonstrate that the underlying wavefunction symmetry of FBs in a LG lattice can be transformed into the atomic/molecular orbital symmetry in a non-LG lattice. We illustrate such orbital-designed topological FBs in three 2D non-LG, square, trigonal, and hexagonal lattices, where the designed orbitals faithfully reproduce the corresponding lattice symmetries of checkerboard, Kagome, and diatomic-Kagome lattices, respectively. Interestingly, systematic design of FBs with a high Chern number is also achieved based on the same principle. Fundamentally our theory enriches the FB physics; practically it significantly expands the scope of FB materials, since most materials have multiple atomic/molecular orbitals at each lattice site, rather than a single s orbital mandated in graph theory and generic lattice models.
Accepted by Physical Review B
References in corpus (20)
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
- Fractional quantum Hall effect in the absence of Landau levels
- Flat bands and Wigner crystallization in the honeycomb optical lattice
- Flat Chern Band in a Two-Dimensional Organometallic Framework
- Epitaxial growth of large-gap quantum spin Hall insulator on semiconductor surface
- Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
- Flat-Bands-Enabled Triplet Excitonic Insulator in a Di-atomic Kagome Lattice
- sd2 Graphene: Kagome Band in Hexagonal lattice
- Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
- Screening 2D materials with topological flat bands
- Kinetic ferromagnetism on a kagome lattice
- New class of flat-band models on tetragonal and hexagonal lattices: Gapped versus crossing flat bands
- Weyl points created by a three-dimensional flat band
- Fragile topology in line-graph lattices with two, three, or four gapped flat bands
- Designing flat-band tight-binding models with tunable multifold band touching points
- Wave-function geometry of band crossing points in two-dimensions
- Methods for constructing parameter-dependent flat band lattices
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- Twisted nodal wires and three-dimensional quantum spin Hall effect in distorted square-net compounds
- Flat Bands Arising from Spin-Orbit Assisted Orbital Frustration
- Interorbital Antisymmetric Hopping Generated Flat Bands on Kagome and Pyrochlore Lattices
- Spinor ice correlation in flat-band electronic states on kagome and pyrochlore lattices with spin-orbit coupling
- Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction