First-principles strategy for electron-phonon coupling in twisted bilayer graphene*

Twisted bilayer graphene (tBLG) systems at certain twisted angles host exotic phenomena such as superconductivity and correlated insulator state. One key question is whether the superconductivity in such systems is phonon-driven or not. However, a moiré unit cell at small twisted angles usually contains over ten thousand of atoms, limiting any quantitative first-principles investigations on the electron-phonon (e-ph) coupling in tBLG. Here we propose a first-principles strategy to accurately compute the e-ph coupling in tBLG where the e-ph matrix elements in the moiré cells are mapped to those in few-atom unit-cells, with controlled approximations. The e-ph coupling is computed using density-functional perturbation theory and GW perturbation theory [1], with the latter includes electron correlation effects in the e-ph matrix elements. This strategy can be generalized to other interactions in different moiré systems while incorporating both intralayer and interlayer effects.

[1] Z. Li, G. Antonius, M. Wu, F. H. da Jornada, and S. G. Louie, Phys. Rev. Lett. 122, 186402 (2019).