Truncated atomic plane wave method for the subband structure calculations of Moiré systems

Abstract

We propose a highly efficient and accurate numerical scheme named Truncated Atomic Plane Wave (TAPW) method to determine the subband structure of Twisted Bilayer Graphene (TBG) inspired by BM model. Our method utilizes real space information of carbon atoms in the moiré unit cell and projects the full tight binding Hamiltonian into a much smaller subspace using atomic plane waves. We present accurate electronic band structures of TBG in a wide range of twist angles together with detailed moiré potential and screened Coulomb interaction at the first magic angle using our new method. Furthermore, we generalize our formalism to solve the problem of low frequency moiré phonons in TBG.

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Cited by in corpus (21)

• Strong Inter-valley Electron-Phonon Coupling in Magic-Angle Twisted Bilayer Graphene
• Twisted bilayer graphene revisited: minimal two-band model for low-energy bands
• Electron-phonon coupling and competing Kekulé orders in twisted bilayer graphene
• Lattice distortions, moiré phonons, and relaxed electronic band structures in magic-angle twisted bilayer graphene
• Engineering the in-plane anomalous Hall effect in Cd${}_3$As${}_2$ thin films
• Electron phonon coupling in the topological heavy fermion model of twisted bilayer graphene
• Moiré optical phonons dancing with heavy electrons in magic-angle twisted bilayer graphene
• DPmoire: A tool for constructing accurate machine learning force fields in moiré systems
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Diagrammatic perturbation approach to moiré bands in twisted bilayer graphene
• Layer Hall counterflow as a model probe of magic-angle twisted bilayer graphene
• Emergence of Cascading Flat Bands in Breathing Superlattices
• Nonflat bands and chiral symmetry in magic-angle twisted bilayer graphene
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Wavefunction textures in twisted bilayer graphene from first principles
• Twisted bilayer graphene from first-principles: structural and electronic properties
• Two-dimensional moiré phonon polaritons
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• General Many-Body Perturbation Framework for Moiré Systems
• Microscopic theory for electron-phonon coupling in twisted bilayer graphene
• Decomposing Electronic Structures in Twisted Multilayers: Bridging Spectra and Incommensurate Wave Functions