Umklapp electron-electron scattering in bilayer graphene moir\'e superlattice

TL;DR

This paper predicts that umklapp electron-electron scattering in bilayer graphene on hBN causes a T^2-dependent resistivity, with the effect strongly influenced by doping, twist angle, and band structure modifications.

Contribution

It introduces a theoretical prediction of umklapp electron-electron scattering effects in bilayer graphene moiré superlattices, highlighting their impact on resistivity behavior.

Findings

Uee scattering causes T^2 resistivity dependence.

Substantial Uee scattering occurs above a doping threshold.

Resistivity peak amplitude varies with superlattice period.

Abstract

Recent experimental advances have been marked by the observations of ballistic electron transport in moir\'e superlattices in highly aligned heterostructures of graphene and hexagonal boron nitride (hBN). Here, we predict that a high-quality graphene bilayer aligned with an hBN substrate features $T^2$-dependent resistivity caused by umklapp electron-electron (Uee) scattering from the moir\'e superlattice, that is, a momentum kick by Bragg scattering experienced by a pair of electrons. Substantial Uee scattering appears upon $p$-doping of the bilayer above a threshold density, which depends on the twist angle between graphene and hBN, and its contribution towards the resistivity grows rapidly with hole density until it reaches a peak value, whose amplitude changes non-monotonically with the superlattice period. We also analyse the influence of an electrostatically induced bandgap in the bilayer and trigonal warping it enhances in the electron dispersion on the electron-electron umklapp scattering.