Intrinsically-multilayer moiré heterostructures

Abstract

We introduce trilayer and multilayer moiré heterostructures that cannot be viewed from the ``moiré-of-moiré" perspective of helically-twisted trilayer graphene. These ``intrinsically trilayer" moiré systems feature periodic modulation of a local quasicrystalline structure. They open the door to realizing moiré heterostructures with vastly more material constituents because they do not constrain the lattice constants of the layers. In this manuscript, we define intrinsically multilayer patterns, provide a recipe for their construction, derive their local configuration space, and connect the visual patterns to physical observables in material systems.

arXiv commentFixed missing figure

References in corpus (79)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Tuning superconductivity in twisted bilayer graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• Cloning of Dirac fermions in graphene superlattices
• Magic continuum in twisted bilayer WSe2
• Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
• Origin of Magic Angles in Twisted Bilayer Graphene
• Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice
• Hubbard model physics in transition metal dichalcogenide moiré bands
• Atomic and electronic reconstruction at van der Waals interface in twisted bilayer graphene
• Anisotropic behaviors of massless Dirac fermions in graphene under periodic potential
• Electric Field Tunable Correlated States and Magnetic Phase Transitions in Twisted Bilayer-Bilayer Graphene
• Spin-polarized Correlated Insulator and Superconductor in Twisted Double Bilayer Graphene
• Quantum anomalous Hall effect from intertwined moiré bands
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Correlated states in twisted double bilayer graphene
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene
• New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
• Strong coupling phases of partially filled twisted bilayer graphene narrow bands
• Band Structure of Twisted Bilayer Graphene: Emergent Symmetries, Commensurate Approximants and Wannier Obstructions
• Continuous Mott transition in semiconductor moiré superlattices
• Quantum Criticality in Twisted Transition Metal Dichalcogenides
• Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
• Relaxation and Domain Formation in Incommensurate 2D Heterostructures
• Magic Angle Hierarchy in Twisted Graphene Multilayers
• Extra Dirac points in the energy spectrum for superlattices on single-layer graphene
• One-Dimensional Moiré Excitons in Transition-Metal Dichalcogenide Heterobilayers
• Topologically Protected Helical States in Minimally Twisted Bilayer Graphene
• Designing Flat Band by Strain
• Band Structure Engineering of 2D Materials using Patterned Dielectric Superlattices
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Band structure and topological property of twisted double bilayer graphenes
• Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer WSe${}_2$
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
• Making Massless Dirac Fermions from Patterned Two-Dimensional Electron Gases
• Transport through a network of topological states in twisted bilayer graphene
• Hartree-Fock study of the moiré Hubbard model for twisted bilayer transition metal dichalcogenides
• One-Dimensional Luttinger Liquids in a Two-Dimensional Moiré Lattice
• One-dimensional flat bands in twisted bilayer germanium selenide
• Twisted bilayer graphene.VI. An Exact Diagonalization Study of Twisted Bilayer Graphene at Non-Zero Integer Fillings
• Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a $k\cdot p$ 2-Band model
• Flat bands and perfect metal in trilayer moiré graphene
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Valley-Polarized Quantum Anomalous Hall State in Moiré MoTe${}_2$/WSe${}_2$ Heterobilayers
• Anisotropic band flattening in graphene with 1D superlattices
• Topological and stacked flat bands in bilayer graphene with a superlattice potential
• Tunable Superlattice in Graphene To Control the Number of Dirac Points
• Moiré of Moiré: Modeling Mechanical Relaxation in Incommensurate Trilayer van der Waals Heterostructures
• Quantum anomalous Hall effect from inverted charge transfer gap
• A moiré superlattice on the surface of a topological insulator
• Chiral Kondo Lattice in Doped MoTe${}_2$/WSe${}_2$ Bilayers
• Flat band in twisted bilayer Bravais lattices
• Gate-tunable two-dimensional superlattices in graphene
• Dynamical Mean Field Theory of Moiré Bilayer Transition Metal Dichalcogenides: Phase Diagram, Resistivity, and Quantum Criticality
• Supermoiré low-energy effective theory of twisted trilayer graphene
• Energy minimization of 2D incommensurate heterostructures
• Symmetry breaking and anomalous conductivity in a double moiré superlattice
• Generalized Kubo Formulas for the Transport Properties of Incommensurate 2D Atomic Heterostructures
• Tunable Stripe Order and Weak Superconductivity in the Moiré Hubbard Model
• Symmetry Origin of Lattice Vibration Modes in Twisted Multilayer Graphene: Phasons vs Moiré Phonons
• Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime
• Dirac-Harper Theory for One Dimensional Moiré Superlattices
• Designer Meron Lattice on the Surface of a Topological Insulator
• Magic angle conditions for twisted 3D topological insulators
• Staggered Pseudo Magnetic Field in Twisted Transition Metal Dichalcogenides: Physical Origin and Experimental Consequences
• Energetic stability and spatial inhomogeneity in the local electronic structure of relaxed twisted trilayer graphene
• Doubled Moiré Flat Bands in Double-twisted Few Layer Graphite
• Effective continuum model of twisted bilayer GeSe and origin of emerging one-dimensional mode
• Anomalous Electrodynamics and Quantum Geometry in the Dirac-Harper model for a Graphene Bilayer

Cited by in corpus (7)

• Multi-scale lattice relaxation in general twisted trilayer graphenes
• Chiral model of twisted bilayer graphene realized in a monolayer
• Multiplicative topological semimetals
• Band theory for heterostructures with interface superlattices
• Electronic analogue of Fourier optics with mass-less Dirac fermions scattered by quantum dot lattice
• Spin and Valley Polarized Multiple Fermi Surfaces of α-RuCl${}_3$/Bilayer Graphene Heterostructure
• Topological domain-wall states from Umklapp scattering in twisted bilayer graphene