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.
12+8 pages
References in corpus (5)
- Origin of band gaps in graphene on hexagonal boron nitride
- Entanglement Spectrum of a Disordered Topological Chern Insulator
- Anderson localization transitions with and without random potentials
- Symmetry breaking in the double moiré superlattices of relaxed twisted bilayer graphene on hexagonal boron nitride
- Misalignment instability in magic-angle twisted bilayer graphene on hexagonal boron nitride
Cited by in corpus (25)
- 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
- Electronic properties of twisted bilayer graphene suspended and encapsulated with hexagonal boron nitride
- Excitonic Chern insulator and kinetic ferromagnetism in MoTe/WSe moiré bilayer
- 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
- Localization via Quasi-Periodic Bulk-Bulk Correspondence
- Higher-order Bragg gaps in the electronic band structure of bilayer graphene renormalized by recursive supermoiré potential
- 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
- Emergence of intrinsically isolated flat bands and their topology in fully relaxed twisted multi-layer graphene
- Designing Moire Patterns by Shearing
- Collective excitations of the Chern-insulator states in commensurate double moiré superlattices of twisted bilayer graphene on hexagonal boron nitride
- Level spacing distribution of localized phases induced by quasiperiodic potentials
- Anomalous universal quantum transport in 2D asymptotic quasiperiodic system
- Energy Spectrum Theory of Incommensurate Systems