Predicting electron-phonon coupling and electronic transport at the moiré 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$100 atoms due to computational cost. Here, we develop an atomistic electronic potential with Holstein- and Peierls-like terms for modeling e-ph interactions and phonon-limited electronic transport that enables the study of moiré systems with thousands of atoms per unit cell. This method can accurately reproduce first-principles e-ph coupling and resistivity in graphene and large-angle twisted bilayer graphene (TBG). Using this approach, we study TBG over a range of twist angles down to 1.6$^\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 moiré materials and other systems with previously inaccessible length scales.

Figures (4)

• Figure 1: (a) E-ph coupling computed in this work, $g_{\nu}(\mathbf{k} \!=\! K, \mathbf{q}) = (\frac{1}{N_b}\sum_{nm} |g_{nm\nu}(\mathbf{k} = K, \mathbf{q})|^2)^{1/2}$ averaged over Dirac-cone bands, plotted on the phonon dispersion for 21.8° TBG. (b) Same plot as in (a), but with phonons and e-ph coupling from DFPT. (c) Resistivity in MLG, calculated with our approach and from DFPT e-ph coupling gao_firstprinciples_2024, in both cases using the RTA.
• Figure 2: (a) Temperature dependent resistivity of 2.0° TBG computed for several electronic fillings (solid lines) and compared to experiments (symbols) chung_transport_2018. (b) Filling-dependent resistivity in 2.0° TBG at several temperatures. The moiré bands are completely filled / empty at $n \!=\! \pm 9.3 \times 10^{12}$ cm$^{-2}$.
• Figure 3: (a) Twist angle dependence of the resistivity at several temperatures for a Fermi energy located halfway to the upper VHS. (b) Twist angle dependence of the e-ph coupling strength $\lambda$ at four fillings.
• Figure 4: Calculated band structure of (a) 13.2°, (b) 3.15°, and (c) 1.61° TBG, respectively. For the same sequence of twist angles, we show the temperature dependent resistivity at several electronic fillings in panels (d)-(f), and the resistivity as a function of electron filling at several temperatures in panels (g)-(i), respectively.