Extended linear-in-$T$ resistivity due to electron-phason scattering in moir\'e superlattices

TL;DR

This paper demonstrates that electron-phason scattering in moiré superlattices causes resistivity to scale linearly with temperature at low temperatures, and also influences thermodynamic properties, providing insights into observed behaviors in twisted bilayer graphene.

Contribution

It reveals how phason modes induce linear-in-T resistivity and specific heat in moiré systems, highlighting a mechanical origin of these phenomena.

Findings

Resistivity scales linearly with temperature due to electron-phason scattering.

Phason contributions lead to a metallic-like linear specific heat at low temperatures.

Implications for understanding linear-in-T resistivity in twisted bilayer graphene.

Abstract

Due to its incommensurate nature, moir\'e superlattices host not only acoustic phonons but also another type of soft collective modes called phasons. Here, we investigate the impact of electron-phason scattering on the transport properties of moir\'e systems. We show that the resistivity can scale linearly with temperature down to temperatures much lower than the Bloch-Gr\"uneisen scale defined by electron kinematics on the Fermi surface. This result stems from the friction between layers, which transfers phason spectral weight to a broad diffusive low-energy peak in the mechanical response of the system. As a result, phason scattering becomes a very efficient channel for entropy production at low temperatures. We also consider the contributions of phasons to thermodynamic properties at low temperatures and find a ''metallic-like'' linear-in-$T$ behavior for the specific heat, despite the fact that this behavior is due to mechanical and not electronic degrees of freedom. We discuss the implications of this finding to reports of linear-in-$T$ resistivity in the phase diagram of twisted bilayer graphene.