Symmetry-based classification of exact flat bands in single and bilayer moiré systems
arXiv:2310.02218 · doi:10.1103/nys8-5mg2
Abstract
We study the influence of spatial symmetries on the appearance and the number of exact flat bands (FBs) in single and bilayer systems with Dirac or quadratic band crossing points, and systematically classify all possible number of exact flat bands in systems with different point group symmetries. We find that a maximum of 6 FBs can be protected by symmetries, and show an example of 6 FBs in a system with QBCP under periodic strain field of point group symmetry. All known examples of exact FBs in single and bilayer systems fall under this classification, including chiral twisted bilayer graphene, and new examples of exact FBs are found. We show the construction of wavefunctions for the highly degenerate FBs, and prove that any such set of FBs are $\mathds{Z}_2$ nontrivial, where all WFs polarized on one sublattice together have Chern number and WFs polarized on the other sublattice together have . These bands also satisfy ideal non-Abelian quantum geometry condition. We further show that, just like in TBG, topological heavy fermion description of the FBs with higher degeneracy is possible as long as the Berry curvature distribution is peaked around a point in the BZ.
References in corpus (65)
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- Maximally-localized generalized Wannier functions for composite energy bands
- Maximally localized Wannier functions: Theory and applications
- Moire bands in twisted double-layer graphene
- Maximally-localized Wannier functions for entangled energy bands
- Wannier90 as a community code: new features and applications
- Topological quantum chemistry
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Origin of Magic Angles in Twisted Bilayer Graphene
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Observation of Fractionally Quantized Anomalous Hall Effect
- Fractional quantum Hall effect in the absence of Landau levels
- Spin-polarized Correlated Insulator and Superconductor in Twisted Double Bilayer Graphene
- Fractional Chern Insulator
- Correlated states in twisted double bilayer graphene
- Integer and fractional Chern insulators in twisted bilayer MoTe2
- Topological Flat Band Models and Fractional Chern Insulators
- All "Magic Angles" Are "Stable" Topological
- Fractional Quantum Hall Physics in Topological Flat Bands
- Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
- The Insulating State of Matter: A Geometrical Theory
- Band geometry of fractional topological insulators
- Correlated Insulating States in Twisted Double Bilayer Graphene
- Electrically tunable correlated and topological states in twisted monolayer-bilayer graphene
- Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
- MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
- Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
- Exact Landau Level Description of Geometry and Interaction in a Flatband
- Topological semimetal in a fermionic optical lattice
- Zoology of Fractional Chern Insulators
- Topological flat band models with arbitrary Chern numbers
- Evidence of Flat Bands and Correlated States in Buckled Graphene Superlattices
- Accurate tight-binding and continuum models for the bands of bilayer graphene
- Visualizing Strain-induced Pseudo magnetic Fields in Graphene through an hBN Magnifying Glass
- Tunable van Hove Singularities and Correlated States in Twisted Trilayer Graphene
- Twisted bilayer graphene. II. Stable symmetry anomaly
- Relations between topology and the quantum metric for Chern insulators
- Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
- Blue Phosphorene Oxide: Strain-tunable Quantum Phase Transitions and Novel 2D Emergent Fermions
- Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
- Multiple topological transitions in twisted bilayer graphene near the first magic angle
- Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
- Multiple and spectrally robust photonic magic angles in reconfigurable α-MoO3 trilayers
- Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
- Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
- Correlated electron-hole State in Twisted Double Bilayer Graphene
- Magic-angle Bilayer Phononic Graphene
- Competing correlated states and abundant orbital magnetism in twisted monolayer-bilayer graphene
- Theta vocabulary I
- Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
- Adiabatic continuity between Hofstadter and Chern insulator states
- Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
- Monolayer MgC: Negative Poisson's ratio and unconventional 2D emergent fermions
- Topological exact flat bands in two dimensional materials under periodic strain
- Topological magnon bands for magnonics
- Realization of a two-dimensional checkerboard lattice in monolayer CuN
- Symmetries as the guiding principle for flattening bands of Dirac fermions
- Higher vortexability: zero field realization of higher Landau levels
- Nearly flat Chern band in periodically strained monolayer and bilayer graphene
- Twisted-bilayer FeSe and the Fe-based superlattices
- Symmetry-broken Chern insulators in twisted double bilayer graphene
- Double and Quadruple Flat Bands tuned by Alternative magnetic Fluxes in Twisted Bilayer Graphene