Electron-phonon and electron-electron interaction effects in twisted bilayer graphene

TL;DR

This paper critically compares continuum many-body theories with experimental data on twisted bilayer graphene, revealing limitations of perturbative approaches and highlighting the potential of nonperturbative methods for understanding electron interactions.

Contribution

It provides a comprehensive critical analysis of electron-phonon and electron-electron interactions in tBLG, emphasizing the failure of leading-order perturbative theories and suggesting alternative nonperturbative approaches.

Findings

Perturbative 1-loop RG theory fails for strong-coupling electron-electron interactions.

Nonperturbative methods like Borel-Padé and 1/N expansion align better with experiments.

Leading-order continuum theory describes electron-phonon interactions well except near van Hove singularities.

Abstract

By comparing with recently available experimental data from several groups, we critically discuss the manifestation of continuum many body interaction effects in twisted bilayer graphene (tBLG) with small twist angles and low carrier densities, which arise naturally within the Dirac cone approximation for the non-interacting band structure. We provide two specific examples of such continuum many body theories: one involving electron-phonon interaction and one involving electron-electron interaction. In both cases, the experimental findings are only partially quantitatively consistent with rather clear-cut leading-order theoretical predictions based on well-established continuum many body theories. We provide a critical discussion, based mainly on the currently available tBLG experimental data, on possible future directions for understanding many body renormalization involving electron-phonon and electron-electron interactions in the system. One definitive conclusion based on the comparison between theory and experiment is that the leading order 1-loop perturbative renormalization group theory completely fails to account for the electron-electron interaction effects in the strong-coupling limit of flatband moir\'e tBLG system near the magic twist angle even at low doping where the Dirac cone approximation should apply. By contrast, approximate nonperturbative theoretical results based on Borel-Pad\'e resummation or $1/N$ expansion seems to work well compared with experiments, indicating rather small interaction corrections to Fermi velocity or carrier effective mass. For electron-phonon interactions, however, the leading-order continuum theory works well except when van Hove singularities in the density of states come into play.