Review of the tight-binding method applicable to the properties of moiré superlattices

Abstract

Moiré superlattices have emerged as a versatile platform for exploring a wide range of ex- otic quantum phenomena. Unlike angstrom-scale materials, the moiré length-scale system contains a large number of atoms, and its electronic structure is significantly modulated by the lattice relaxation. These features pose a huge theoretical challenge. Among the available theoretical approaches, tight-binding (TB) methods are widely employed to predict the electronic, transport, and optical properties of systems such as twisted graphene, twisted transition-metal dichalcogenides (TMDs), and related moiré materials. In this review, we pro- vide a comprehensive overview of atomistic TB Hamiltonians and the numerical techniques commonly used to model graphene-based, TMD-based and hBN-based moiré superlattices. We also discuss the connection between atomistic TB descriptions and effective low-energy continuum models. Two examples of different moiré materials and geometries are provided to emphasize the advantages of the TB methods. This review is intended to serve as a theoretical and practical guide for those seeking to apply TB methods to the study of various properties of moiré superlattices.

Invitation from PCCP

References in corpus (133)

• Chiral tunneling and the Klein paradox in graphene
• A tight-binding approach to uniaxial strain in graphene
• The electronic properties of bilayer graphene
• The Kernel Polynomial Method
• Optical detection of Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices
• Magic continuum in twisted bilayer WSe2
• Flat Bands in Slightly Twisted Bilayer Graphene
• Graphene Bilayers with a Twist
• Detecting Topological Currents in Graphene Superlattices
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Quasiparticle band structure and tight-binding model for single- and bilayer black phosphorus
• Abundance of correlated insulating states at fractional fillings of WSe${}_2$/WS${}_2$ moiré superlattices
• Continuum Model of the Twisted Bilayer
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• Quantum anomalous Hall effect from intertwined moiré bands
• Finite temperature lattice properties of graphene beyond the quasiharmonic approximation
• Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene
• Decoupling superconductivity and correlated insulators in twisted bilayer graphene
• Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene
• Interfacial ferroelectricity in marginally twisted 2D semiconductors
• Flat bands in twisted bilayer transition metal dichalcogenides
• Superconductivity without insulating states in twisted bilayer graphene stabilized by monolayer WSe${}_2$
• Origin of band gaps in graphene on hexagonal boron nitride
• Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride
• Numerical studies of confined states in rotated bilayers of graphene
• Atomic reconstruction and moiré patterns in transition metal dichalcogenide van der Waals heterostructures
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• Electronic properties of graphene hexagonal boron nitride moiré superlattice
• Modeling electronic structure and transport properties of graphene with resonant scattering centers
• Deep-Learning Density Functional Theory Hamiltonian for Efficient ab initio Electronic-Structure Calculation
• Imaging moiré flat bands in 3D reconstructed WSe2/WS2 superlattices
• Imaging orbital ferromagnetism in a moiré Chern insulator
• $\Gamma$-Valley Transition-Metal-Dichalcogenide Moirè Bands
• Stability of boron nitride bilayers: Ground state energies, interlayer distances, and tight-binding description
• Observation of an intrinsic bandgap and Landau level renormalization in graphene/boron-nitride heterostructures
• Superconductivity in twisted bilayer WSe${}_2$
• Continuum models for twisted bilayer graphene: the effects of lattice deformation and hopping parameter
• Spin-orbit driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene
• Band structure and insulating states driven by the Coulomb interaction in twisted bilayer graphene
• Interlayer interaction in general incommensurate atomic layers
• Tunable electrochemistry with moiré flat bands and topological defects at twisted bilayer graphene
• Real-space calculation of the conductivity tensor for disordered topological matter
• General framework for E(3)-equivariant neural network representation of density functional theory Hamiltonian
• Lattice reconstruction induced multiple ultra-flat bands in twisted bilayer WSe2
• Electronic structures, charge transfer and charge orders in twisted transition metal dichalcogenide bilayers
• Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a $k\cdot p$ 2-Band model
• Continuum model for relaxed twisted bilayer graphenes and moiré electron-phonon interaction
• Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
• Gate-Defined Josephson Junctions in Magic-Angle Twisted Bilayer Graphene
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Excitons in mesoscopically reconstructed moiré heterostructures
• Moiré band model and band gaps of graphene on hexagonal boron nitride
• Emulating heavy fermions in twisted trilayer graphene
• Transferable E(3) equivariant parameterization for Hamiltonian of molecules and solids
• Dodecagonal bilayer graphene quasicrystal and its approximants
• Double moiré with a twist: super-moiré in encapsulated graphene
• Kondo lattice model in magic-angle twisted bilayer graphene
• KITE: high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures
• Spectroscopy Signatures of Electron Correlations in a Trilayer Graphene/hBN Moiré Superlattice
• Tunable large Berry dipole in strained twisted bilayer graphene
• Band structure of twisted bilayer graphene on hexagonal boron nitride
• Heterostrain rules the flat-bands in magic-angle twisted graphene layers
• Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory
• Rotational and Dilational Reconstruction in Transition Metal Dichalcogenide Moiré Bilayers
• Unconventional Superconductivity in Magic-Angle Twisted Trilayer Graphene
• Deep-learning electronic-structure calculation of magnetic superstructures
• Multi-ultraflatbands tunability and effect of spin-orbit coupling in twisted bilayer transition metal dichalcogenides
• General continuum model for twisted bilayer graphene and arbitrary smooth deformations
• Deep learning tight-binding approach for large-scale electronic simulations at finite temperatures with $ab$ $initio$ accuracy
• An accurate description of the structural and electronic properties of twisted bilayer graphene-boron nitride heterostructures
• Moire Potential, Lattice Relaxation and Layer Polarization in Marginally Twisted MoS2 Bilayers
• Pseudo-magnetic fields, particle-hole asymmetry, and microscopic effective continuum Hamitonians of twisted bilayer graphene
• Visualizing moiré ferroelectricity via plasmons and nano-photocurrent in graphene/twisted-WSe2 structures
• Electronic localization in twisted bilayer MoS${}_2$ with small rotation angle
• Flat bands, strains, and charge distribution in twisted-bilayer hBN
• Strain induced quasi-unidimensional channels in twisted moiré lattices
• Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe${}_2$
• Spectral characterization of magic angles in twisted bilayer graphene
• Continuum effective Hamiltonian for graphene bilayers for an arbitrary smooth lattice deformation from microscopic theories
• Observation of Rydberg moiré excitons
• Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene
• Multiple Chern bands in twisted MoTe${}_2$ and possible non-Abelian states
• Electronic structure calculations of twisted multi-layer graphene superlattices
• Tuning band gaps in twisted bilayer MoS${}_2$
• Universal Machine Learning Kohn-Sham Hamiltonian for Materials
• Flat-band ferromagnetism in twisted bilayer graphene
• Effect of bilayer stacking on the atomic and electronic structure of twisted double bilayer graphene
• Designing Moiré Patterns by Strain
• Lasing of Moiré Trapped MoSe${}_2$/WSe${}_2$ Interlayer Excitons Coupled to a Nanocavity
• Unconventional Nonlocal Relaxation Dynamics in a Twisted Graphene Moire Superlattice
• Collective excitations and plasmon spectrum in twisted bilayer graphene near the magic angle
• Twistronics versus straintronics in twisted bilayers of graphene and transition metal dichalcogenides
• Electronic localization in small-angle twisted bilayer graphene
• Lattice relaxation, mirror symmetry and magnetic field effects on ultraflat bands in twisted trilayer graphene
• Moiré induced topology and flat bands in twisted bilayer WSe${}_2$: A first-principles study
• Topological electronic crystals in twisted bilayer-trilayer graphene
• Truncated atomic plane wave method for the subband structure calculations of Moiré systems
• Electronic properties of twisted bilayer graphene suspended and encapsulated with hexagonal boron nitride
• Cavity-Quantum Electrodynamics with Moiré Flatband Photonic Crystals
• Twisted bilayer graphene revisited: minimal two-band model for low-energy bands
• Flat-band plasmons in twisted bilayer transition metal dichalcogenides
• Existence of the first magic angle for the chiral model of bilayer graphene
• Spin-orbit coupling-enhanced valley ordering of malleable bands in twisted bilayer graphene on WSe2
• Flat bands, electron interactions and magnetic order in magic-angle mono-trilayer graphene
• Engineering band structures of two-dimensional materials with remote moire ferroelectricity
• Full Slonczewski-Weiss-McClure parametrization of few-layer twistronic graphene
• Time-reversal versus chiral symmetry breaking in twisted bilayer graphene
• Electronic structure of 30° twisted double bilayer graphene
• Extended magic phase in twisted graphene multilayers
• Domain-dependent surface adhesion in twisted few-layer graphene: Platform for moiré-assisted chemistry
• Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula
• Magnetic phases from competing Hubbard and extended Coulomb interactions in twisted bilayer graphene
• Topological flat bands in a family of multilayer graphene moiré lattices
• Efficient Chebyshev polynomial approach to quantum conductance calculations: Application to twisted bilayer graphene
• Weak Coupling Theory of Magic-Angle Twisted Bilayer Graphene
• Optical activity and transport in twisted bilayer graphene: the essence of spatial dispersion effects
• Evolution of flat bands in MoSe${}_2$/WSe${}_2$ moiré lattices: A study combining machine learning and band unfolding methods
• One-Dimensional Moiré Physics and Chemistry in Heterostrained Bilayer Graphene
• Ising superconductivity induced from spin-selective valley symmetry breaking in twisted trilayer graphene
• Nematic versus Kekulé phases in twisted bilayer graphene under hydrostatic pressure
• DPmoire: A tool for constructing accurate machine learning force fields in moiré systems
• General Electronic Structure Calculation Method for Twisted Systems
• Seeing moiré: convolutional network learning applied to twistronics
• Tuning flat bands by interlayer interaction, spin-orbital coupling, and external fields in twisted homotrilayer MoS${}_2$
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Gate-defined superconducting channel in magic-angle twisted bilayer graphene
• Emergence of flat bands in the quasicrystal limit of boron nitride twisted bilayers
• Diagrammatic perturbation approach to moiré bands in twisted bilayer graphene
• Short vs. long range exchange interactions in twisted bilayer graphene
• Moiré flat bands and antiferroelectric domains in lattice relaxed twisted bilayer hexagonal boron nitride under perpendicular electric fields
• Origin of magic angles in twisted bilayer graphene: The magic ring