Quasiperiodicity, band topology, and moiré graphene
arXiv:2011.06034 · doi:10.1103/PhysRevB.103.115110
Abstract
A number of moiré graphene systems have nearly flat topological bands where electron motion is strongly correlated. Though microscopically these systems are only quasiperiodic, they can typically be treated as translation invariant to an excellent approximation. Here we reconsider this question for magic angle twisted bilayer graphene that is nearly aligned with a hexagonal boron nitride(h-BN) substrate. We carefully study the effect of the periodic potential induced by h-BN on the low energy physics. The combination of this potential and the moiré lattice produced by the twisted graphene generates a quasi-periodic term that depends on the alignment angle between h-BN and the moiré graphene. We find that the alignment angle has a significant impact on both the band gap near charge neutrality and the behavior of electrical transport. We also introduce and study toy models to illustrate how a quasi-periodic potential can give rise to localization and change in transport properties of topological bands.
arXiv comment12+8 pages
References in corpus (40)
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- Maximally localized Wannier functions: Theory and applications
- Anderson localization of a non-interacting Bose-Einstein condensate
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
- Intrinsic quantized anomalous Hall effect in a moiré heterostructure
- Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice
- Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
- Correlated states in twisted double bilayer graphene
- Nearly Flat Chern Bands in Moiré Superlattices
- Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
- Flat bands in twisted bilayer transition metal dichalcogenides
- Origin of band gaps in graphene on hexagonal boron nitride
- A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
- Band Structure of Twisted Bilayer Graphene: Emergent Symmetries, Commensurate Approximants and Wannier Obstructions
- Ab-Initio Theory of Moiré Superlattice Bands in Layered Two-Dimensional Materials
- Entanglement Spectrum of a Disordered Topological Chern Insulator
- Delocalization of a disordered bosonic system by repulsive interactions
- Electrically tunable correlated and topological states in twisted monolayer-bilayer graphene
- Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
- Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
- Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model
- Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands
- Localization in a quantum spin Hall system
- Critical and bicritical properties of Harper's equation with next nearest neighbor coupling
- Localization transitions and mobility edges in coupled Aubry-André chains
- Bridging Hubbard Model Physics and Quantum Hall Physics in Trilayer Graphene/h-BN moiré superlattice
- Anderson localization transitions with and without random potentials
- Band structure of twisted bilayer graphene on hexagonal boron nitride
- Magic-angle semimetals
- Weyl semimetal to metal phase transitions driven by quasiperiodic potentials
- Universality and Quantum Criticality in Quasiperiodic Spin Chains
- Moire Localization in Two Dimensional Quasi-Periodic Systems
- Magic-Angle Semimetals with Chiral Symmetry
- The quasi-periodic quantum Ising transition in 1D
- Flat Topological Bands and Eigenstate Criticality in a Quasiperiodic Insulator
- Symmetry breaking in the double moiré superlattices of relaxed twisted bilayer graphene on hexagonal boron nitride
- Quantum criticality in Ising chains with random hyperuniform couplings
- Misalignment instability in magic-angle twisted bilayer graphene on hexagonal boron nitride
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- Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal
- Anomalous Hall effect at half filling in twisted bilayer graphene
- Band Structure and Superconductivity in Twisted Trilayer Graphene
- An accurate description of the structural and electronic properties of twisted bilayer graphene-boron nitride heterostructures
- Flat bands, strains, and charge distribution in twisted-bilayer hBN
- Flat Topological Bands and Eigenstate Criticality in a Quasiperiodic Insulator
- Excitonic Chern insulator and kinetic ferromagnetism in MoTe/WSe moiré bilayer
- Electronic properties of twisted bilayer graphene suspended and encapsulated with hexagonal boron nitride
- Electron-phonon coupling and competing Kekulé orders in twisted bilayer graphene
- Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions
- Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene
- Extended magic phase in twisted graphene multilayers
- Energetic stability and spatial inhomogeneity in the local electronic structure of relaxed twisted trilayer graphene
- Higher-order Bragg gaps in the electronic band structure of bilayer graphene renormalized by recursive supermoiré potential
- Localization via Quasi-Periodic Bulk-Bulk Correspondence
- Quasidisorder Induced Topology
- From topological phase to Anderson localization in a two-dimensional quasiperiodic system
- Deterministic fabrication of graphene hexagonal boron nitride moiré superlattices
- Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
- Quasiperiodic circuit quantum electrodynamics
- Designing Moire Patterns by Shearing
- Emergence of intrinsically isolated flat bands and their topology in fully relaxed twisted multi-layer graphene
- Collective excitations of the Chern-insulator states in commensurate double moiré superlattices of twisted bilayer graphene on hexagonal boron nitride
- Anomalous universal quantum transport in 2D asymptotic quasiperiodic system
- Level spacing distribution of localized phases induced by quasiperiodic potentials
- Energy Spectrum Theory of Incommensurate Systems