Electron-Phonon Coupling and Electronic Transport at the Moire Scale from a First-Principles Based Atomistic Tight-Binding Approach

First-principles calculations of electron-phonon (e-ph) coupling and electronic transport accurately describe many classes of materials, but are computationally limited to systems of a few tens of atoms. Here, we develop a tight-binding ansatz to the e-ph coupling with Peierls and Holstein terms for twisted bilayer graphene (TBG), fit by first-principles interactions. Combined with a tight-binding Hamiltonian and atomic force field, this approach enables calculations of electron transport at large scales in TBG. We demonstrate good agreement with first-principles calculations of the e-ph coupling and resistivity in graphene and large angle TBG. We then use our method to study resistivity in TBG over a range of twist angles down to 1.6° (5044 atoms per unit cell), showing the evolution of transport properties in the phonon-limited Boltzmann picture as the electronic energy scale is decreased. For 1.6° TBG, the predicted resistivity is approximately five times lower than experiments, suggesting the importance of factors such as modified screening, correlation effects, beyond-quasiparticle transport, and other scattering mechanisms. Our work outlines an approach to extend the accuracy of first principles e-ph coupling and transport to new materials with previously inaccessible system sizes.