Fractal energy gaps and topological invariants in hBN/Graphene/hBN double moiré systems
arXiv:2105.04948 · doi:10.1103/PhysRevB.104.035306
Abstract
We calculate the electronic structure in quasiperiodic double-moiré systems of graphene sandwiched by hexagonal boron nitride, and identify the topological invariants of energy gaps. We find that the electronic spectrum contains a number of minigaps, and they exhibit a recursive fractal structure similar to the Hofstadter butterfly when plotted against the twist angle. Each of the energy gaps can be characterized by a set of integers, which are associated with an area in the momentum space. The corresponding area is geometrically interpreted as a quasi Brillouin zone, which is a polygon enclosed by multiple Bragg planes of the composite periods and can be uniquely specified by the plain wave projection in the weak potential limit.
arXiv comment17 pages, 11 figures
References in corpus (45)
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Boron nitride substrates for high-quality graphene electronics
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- Moire bands in twisted double-layer graphene
- Tuning superconductivity in twisted bilayer graphene
- Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
- Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
- Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
- Graphene bilayer with a twist: electronic structure
- Cloning of Dirac fermions in graphene superlattices
- Topological States and Adiabatic Pumping in Quasicrystals
- Flat Bands in Slightly Twisted Bilayer Graphene
- Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
- Topological Defects and Gapless Modes in Insulators and Superconductors
- Localization of Dirac electrons by Moire patterns in graphene bilayers
- Commensuration and Interlayer Coherence in Twisted Bilayer Graphene
- Electronic structure of turbostratic graphene
- Electric field tunable unconventional superconductivity in alternating twist magic-angle trilayer graphene
- Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene
- Dirac Electrons in a Dodecagonal Graphene Quasicrystal
- Numerical studies of confined states in rotated bilayers of graphene
- Generic Miniband Structure of Graphene on a Hexagonal Substrate
- Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids
- Ab-Initio Theory of Moiré Superlattice Bands in Layered Two-Dimensional Materials
- Electronic properties of graphene hexagonal boron nitride moiré superlattice
- Zero Energy Modes and Gate-Tunable Gap in Graphene on hexagonal Boron Nitride
- Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
- Tunable crystal symmetry in graphene-boron nitride heterostructures with coexisting moiré superlattices
- Twisted Trilayer Graphene: a Precisely Tunable Platform for Correlated Electrons
- Interlayer interaction in general incommensurate atomic layers
- New generation of moiré superlattices in doubly aligned hBN/graphene/hBN heterostructures
- In situ twistronics of van der Waals heterostructures
- Composite super-moiré lattices in double aligned graphene heterostructures
- Quasicrystalline electronic states in 30 rotated twisted bilayer graphene
- Moiré Commensurability and the Quantum Anomalous Hall Effect in Twisted Bilayer Graphene on Hexagonal Boron Nitride
- Double moiré with a twist: super-moiré in encapsulated graphene
- Heterostructure bilayer graphene-hBN: Interplay between misalignment, interlayer asymmetry, and trigonal warping
- Topological charge pumping in twisted bilayer graphene
- Topological charge pumping by sliding moiré pattern
- Electron-hole asymmetry and band gaps of commensurate double moire patterns in twisted bilayer graphene on hexagonal boron nitride
- Topological Sliding Moiré Heterostructure
- Enhanced electron-phonon coupling in doubly aligned hexagonal boron nitride bilayer graphene heterostructure
- Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries
- Brillouin zone labelling for quasicrystals
- Heteromoiré Engineering on Magnetic Bloch Transport in Twisted Graphene Superlattices
Cited by in corpus (18)
- Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal
- Multi-scale lattice relaxation in general twisted trilayer graphenes
- 3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect
- Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization
- Moiré phonons in graphene/hexagonal boron nitride moiré superlattice
- Extended magic phase in twisted graphene multilayers
- Higher-order Bragg gaps in the electronic band structure of bilayer graphene renormalized by recursive supermoiré potential
- Electric field-tunable layer polarization in graphene/boron nitride twisted quadrilayer superlattices
- Topological gap labeling with the third Chern numbers in three-dimensional quasicrystals
- Characterization of a graphene-hBN superlattice field effect transistor
- Strong gate-tunability of flat bands in bilayer graphene due to moiré encapsulation between hBN monolayers
- Ferromagnetically ordered states in the Hubbard model on the hexagonal golden-mean tiling
- Hexagonal and trigonal quasiperiodic tilings
- Moiré fractals in twisted graphene layers
- Gap labeling theorem for multilayer thin film heterostructures
- Energy Spectrum Theory of Incommensurate Systems
- Electric field tunable bands in doubly aligned bilayer graphene hBN moire superlattice
- One-dimensional moiré engineering in zigzag graphene nanoribbons on hBN