Low-temperature thermal transport in moiré superlattices

We calculate the thermal conductivity of various twisted bilayer systems using a continuum approach and the semiclassical transport theory. In the low-temperature regime where the phonons' mean free path is approximately constant, we find a significant reduction of thermal conductivity contributed by the in-plane acoustic phonons when the twist angle is near 0. This occurs as half of the phonons are renormalized with lower group velocities than the original longitudinal and transverse acoustic phonons of the constituent monolayers. The reduction turns into enhancement near the zero-temperature limit as thermal conductivity becomes inversely proportional to the phonon velocity. Altogether, we show that these changes lead to a characteristic temperature dependence that deviates from the quadratic behavior of in-plane acoustic phonons in two-dimensional systems.