Wide-range $T^2$ resistivity and umklapp scattering in moir\'e graphene

TL;DR

This paper explains the strong temperature-dependent resistivity in moiré graphene as arising from enhanced electron-electron umklapp scattering due to compact Wannier orbitals, predicting a T^2 resistivity growth and large Kadowaki-Woods ratios.

Contribution

It introduces a model linking Wannier orbital size to umklapp scattering strength, providing a new explanation for resistivity behavior in moiré superlattices.

Findings

Resistivity in moiré graphene grows as T^2 due to umklapp scattering.

Large Kadowaki-Woods ratios indicate strong electron-electron umklapp processes.

Smaller Wannier orbitals lead to increased resistivity and scattering.

Abstract

We argue that the unusually strong electron-electron interactions in the narrow bands in moir\'e superlattices originate from compact Wannier orbitals. Enhanced overlaps of electronic wavefunctions, enabled by such orbitals, result in a strong el-el superlattice umklapp scattering. We identify the umklapp scattering processes as a source of the strong temperature-dependent resistivity observed in these systems. In a simple model, the umklapp scattering predicts a $T$-dependent resistivity that grows as $T^2$ and is getting bigger as the Wannier orbital radius decreases. We quantify the enhancement in el-el scattering by the Kadowaki-Woods (KW) ratio, a quantity that is sensitive to umklapp scattering but, helpfully, insensitive to the effects due to the high density of electronic states. Our analysis predicts anomalously large KW ratio values that clearly indicate the importance of the umklapp el-el processes and their impact on the $T$-dependent resistivity.