Predicting electron-phonon coupling and electronic transport at the moir\'e scale in twisted bilayer graphene

Abstract

First-principles calculations can accurately describe electron-phonon (e-ph) interactions and electronic transport in a wide range of materials, but are currently limited to unit cells with up to $\sim$100 atoms due to computational cost. Here, we develop an atomistic electronic potential with Holstein- and Peierls-like terms for modeling e-ph interactions and phonon-limited electronic transport that enables the study of moir\'e systems with thousands of atoms per unit cell. This method can accurately reproduce first-principles e-ph coupling and resistivity in graphene and large-angle twisted bilayer graphene (TBG). Using this approach, we study TBG over a range of twist angles down to 1.6$^\circ$ (5044-atom unit cell), and report the evolution of e-ph interactions and phonon-limited resistivity with twist angle. The predicted resistivity increases by two orders of magnitude between 13.2$^\circ$ and 1.6$^\circ$, driven by the progressive reduction of the electronic energy scale. Our calculations can predict key experimental trends in 2.0$^\circ$ and 1.6$^\circ$ TBG, including the resistivity and its dependence on temperature and band filling. Our work establishes a scalable approach for quantitative studies of e-ph interactions and transport in moir\'e materials and other systems with previously inaccessible length scales.