Resonance Raman enhancement by the intralayer and interlayer electron-phonon processes in twisted bilayer graphene

Twisted bilayer graphene is a fascinating system due to the possibility of tuning the electronic and optical properties by controlling the twisting angle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}θ between the layers. The coupling between the Dirac cones of the two graphene layers gives rise to van Hove singularities (vHs) in the density of electronic states, whose energies vary with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}θ. Raman spectroscopy is a fundamental tool to study twisted bilayer graphene (TBG) systems since the Raman response is hugely enhanced when the photons are in resonance with transition between vHs and new peaks appear in the Raman spectra due to phonons within the interior of the Brillouin zone of graphene that are activated by the Moiré superlattice. It was recently shown that these new peaks can be activated by the intralayer and the interlayer electron–phonon processes. In this work we study how each one of these processes enhances the intensities of the peaks coming from the acoustic and optical phonon branches of graphene. Resonance Raman measurements, performed in many different TBG samples with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}θ between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4^{\circ }$$\end{document}4∘ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$16^{\circ }$$\end{document}16∘ and using several different laser excitation energies in the near-infrared (NIR) and visible ranges (1.39–2.71 eV), reveal the distinct enhancement of the different phonons of graphene by the intralayer and interlayer processes. Experimental results are nicely explained by theoretical calculations of the double-resonance Raman intensity in graphene by imposing the momentum conservation rules for the intralayer and the interlayer electron–phonon resonant conditions in TBGs. Our results show that the resonant enhancement of the Raman response in all cases is affected by the quantum interference effect and the symmetry requirements of the double resonance Raman process in graphene.