Truncated atomic plane wave method for subband structure calculations of moir? systems

WQ Miao and C Li and X Han and D Pan and X Dai, PHYSICAL REVIEW B, 107, 125112 (2023).

DOI: 10.1103/PhysRevB.107.125112

We propose a highly efficient and accurate numerical scheme named the truncated atomic plane wave method to determine the subband structure of twisted bilayer graphene (TBG) inspired by the Bistritzer-MacDonald model. Our method utilizes real-space information of carbon atoms in the moire unit cell and projects the full tight-binding Hamiltonian into a much smaller subspace using atomic plane waves. Using our method, we are able to present accurate electronic band structures of TBG in a wide range of twist angles together with the detailed moire potential and screened Coulomb interaction at the first magic angle. Furthermore, we generalize our formalism to solve the problem of low-frequency moire phonons in TBG.

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