Continuum model for relaxed twisted bilayer graphenes and moir\'{e} electron-phonon interaction

TL;DR

This paper develops an analytic continuum model for twisted bilayer graphene that accurately captures electronic structures and electron-phonon interactions, revealing enhanced coupling at low twist angles due to superlattice effects.

Contribution

The authors derive a general continuum model for lattice deformations and electron-phonon interactions in twisted bilayer graphene, extending previous models to arbitrary lattice relaxations.

Findings

Model accurately describes band structures of relaxed twisted bilayer graphene.

Electron-phonon coupling is significantly enhanced at low twist angles.

Derived explicit expressions for electron-phonon matrix elements and phonon modes.

Abstract

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 moir\'{e} band states and the moir\'{e} phonon modes. By numerical calculation, we find that the electron-phonon coupling and phonon mediated electron-electron interaction are significantly enhanced in low twist angles due to the superlattice hybridization.