Effective continuum model for relaxed twisted bilayer graphene and moiré electron-phonon interaction

We construct an analytic continuum model to describe the electronic structure and the electron-phonon interaction in twisted bilayer graphenes with arbitrary lattice deformation. Starting from the tight-binding model, we derive the interlayer Hamiltonian in the presence of general lattice displaceme...

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Bibliographic Details
Published in:Physical review. B 2020-05, Vol.101 (19), p.1, Article 195425
Main Authors: Koshino, Mikito, Nam, Nguyen N. T.
Format: Article
Language:English
Subjects:
Bilayers
Continuum modeling
Coupling
Deformation
Displacements (lattice)
Electron phonon interactions
Electronic structure
Electrons
Graphene
Interlayers
Lattice vibration
Phonons
Superlattices
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Summary:We construct an analytic continuum model to describe the electronic structure and the electron-phonon interaction in twisted bilayer graphenes with arbitrary lattice deformation. Starting from the tight-binding model, we derive the interlayer Hamiltonian in the presence of general lattice displacement and obtain a long-wavelength continuum expression for smooth deformation. We show that the continuum model correctly describes the band structures of the lattice-relaxed twisted bilayer graphenes. We apply the formula to the phonon vibration and derive an explicit expression of the electron-phonon matrix elements between the moiré band states and the moiré phonon modes. By numerical calculation, we find that the electron-phonon coupling is significantly enhanced in low twist angles due to the superlattice hybridization. At the magic angle, in particular, the phonon-mediated electron-electron interaction is found to be comparable to the order of the inverse density of states, suggesting that the system is in the strong coupling regime.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.101.195425