The role of electron-phonon coupling in the superconductivity of twisted bilayer graphene

The origin of superconductivity in twisted bilayer graphene (tBLG) has been a topic of heated debate since its discovery. In magic-angle tBLG, the electronic bands significantly flatten, leading to enhanced electronic correlation, a potential precursor to superconductivity. However, the role of electron-phonon coupling has often been overlooked. To accurately describe electron-phonon coupling in moiré systems, there are nearly insurmountable challenges related to the incommensurability at general twist angles and the large number of degrees of freedom, including both electron and phonon momenta. In this work, we overcome these computational challenges by employing a first-principles-based multi-scale continuum model to accurately and efficiently describe electron-phonon coupling due to moiré phonons in twisted bilayer graphene. We estimate the twist-angle dependence of the superconducting critical temperature without relying on an adiabatic approximation.