Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene

By M. Koshino, N. Yuan, Takashi Koretsune, M. Ochi, K. Kuroki, Liang Fu. Physical Review X, 2018

525 citations recorded by the source corpus.

We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tight-binding model on the emergent honeycomb lattice. We found the Wannier state takes a peculiar three-peak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per super cell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which would possibly lead to an unconventional many-body state.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/52609414ea6f8943ada2d5ed61e8b56221f8f66d

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Citations in the corpus

High-temperature topological superconductivity in twisted double-layer copper oxides (2020, background): “In both cases, the observed behaviour is thought to reflect a subtle interplay between the band structure energetics and topology brought about by the Moiré patterns, electron-electron interactions and disorder [8–17].”
Flat bands, strange metals and the Kondo effect (2023, unknown): “1.”
Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions (2018, methodology): “[5, 18, 21] is actually artificial: the difference is purely due to a different choice of the point-group center, and these results are consistent after converting to the same convention.”
Origin of Magic Angles in Twisted Bilayer Graphene. (2018, background): “In reality, for TBG at tiny twist angles the gap opens and also wAA/wAB is supressed due to lattice relaxation effects [21, 38, 42].”