Extended linear-in-T resistivity due to electron-phason scattering in moiré superlattices

We show that scattering of electrons off of phason modes in incommensurate moiré superlattices, such as twisted bilayer graphene, can give rise to a large, linear-in-T resistivity down to very low temperatures. This mechanism contains features common to other two mechanisms usually invoked to explain linear-in-T resistivity: phonons and quantum critical fluctuations. Indeed, while phasons are similar to acoustic phonons, they result from a global invariance of the free energy that does not correspond to a microscopic symmetry of the Hamiltonian, hence their dynamics are not protected by a local conservation law. Consequently, phasons are generically overdamped at long wavelengths, like quantum critical fluctuations in metals. The associated transfer of spectral weight to low energies makes phason scattering a very efficient channel for entropy production at low temperatures. In particular, the resistivity remains linear down to a newly identified scale T* that can be lower than the Bloch-Grüneisen temperature, below which a quadratic-in-T behavior emerges. Phasons should also dominate other thermodynamic and transport properties at low temperatures, such as the specific heat and the thermal conductivity.