A Monte Carlo study of the electron-phonon problem in twisted bilayer graphene

Recent progress in experiment and theory constrains the pairing symmetry of the superconducting order parameter in twisted bilayer graphene (TBG); however, the pairing mechanism remains more elusive. We study the effects of electron-phonon interactions in a continuum model of TBG near the magic angle, addressing the possibility of phonon-mediated superconductivity. Additionally, we critically examine the possibility of other symmetry-broken states, such as charge-density-wave and nematic phases. The model is free of the infamous fermion sign problem and is thus amenable to solution by the unbiased, numerically exact determinant quantum Monte Carlo method.