Low-temperature thermal transport in moir\'e superlattices

We calculate the phonon thermal conductivity of various moir\'e bilayer systems using a continuum approach and the semiclassical transport theory. When the twist angle is close to 0, we observe a significant reduction of thermal conductivity in a particular low-temperature regime. This reduction is attributed to a moir\'e-induced reconstruction of acoustic phonon bands and associated decrease of the group velocity. Conversely, in the zero temperature limit, the thermal conductivity is enhanced by moir\'e effect, surpassing the original values in non-moir\'e counterparts. These changes result in a characteristic temperature dependence which deviates from the quadratic behavior in intrinsic two-dimensional systems.