Acoustic phonon contribution to the resistivity of twisted bilayer graphene

We calculate the contribution to the doping ($n$) and temperature ($T$) dependence of the electrical resistivity of twisted bilayer graphene (TBLG) due to scattering by acoustic phonons. Our calculation retains the full Bistritzer-MacDonald (BM) band structure, with a focus on understanding the role of the complicated geometric features present in the BM band structure on electronic transport theory. We find that the band geometry plays an important role in determining the resistivity, giving an intricate dependence on both $n$ and $T$ that mirrors features in the band structure and complicates the Bloch-Gr\"{u}neisen (BG) crossover. Our calculations predict pronounced departures from the standard simplistic expectation of a linear $T$-dependence above the BG crossover. In particular, we are able to explain the presence of the resistance peaks that have been observed in experiment, as well as quantitatively predict the temperatures at which they occur. Our calculated theoretical results are germane to an ongoing debate over the existence of a strange metal state in TBLG by providing a quantitatively accurate theory for the TBLG resistivity at finite temperatures.