Origin of Magic Angles in Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) was recently shown to host superconductivity when tuned to special "magic angles" at which isolated and relatively flat bands appear. However, until now the origin of the magic angles and their irregular pattern have remained a mystery. Here we report on a fundamental continuum model for TBG which features not just the vanishing of the Fermi velocity, but also the perfect flattening of the entire lowest band. When parametrized in terms of α∼1/θ, the magic angles recur with a remarkable periodicity of Δα≃3/2. We show analytically that the exactly flat band wave functions can be constructed from the doubly periodic functions composed of ratios of theta functions-reminiscent of…

• NS
  National Science Foundation

  Award: 1411343
• UD
  U.S. Department of Energy

  Award: de-sc0007870
• SN
  Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

  Award: P2ELP2_175278
• MU
  Multidisciplinary University Research Initiative

  Award: W911NF-14-1-0003
• AR
  Army Research Office