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

TL;DR

This paper introduces a scalable atomistic modeling approach to accurately predict electron-phonon interactions and electronic transport in large moiré systems like twisted bilayer graphene, capturing key experimental trends across various twist angles.

Contribution

The authors develop an atomistic potential that enables first-principles accuracy in large moiré systems, overcoming previous computational limitations.

Findings

Resistivity increases by two orders of magnitude from 13.2° to 1.6° twist angles.

Method accurately reproduces experimental trends in resistivity and temperature dependence.

Resistivity reduction is driven by the decreasing electronic energy scale at smaller twist angles.

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.