Corrugation effect, Dirac cone splitting, and plasmon properties of biased twisted bilayer graphene

The unconventional behaviors observed in twisted bilayer graphene (TBG) at special ``magic angles'' characterized by the vanishing Fermi velocity make TBG an intriguing platform for the study of correlated phenomena. Here, on the basis of an effective continuum model, we propose an analytic expression of the Fermi velocity based on which we demonstrate that the first magic angle of TBG is independent of the corrugation effect. We also correlate analytically the Dirac cone splitting of the biased TBG to the external electric field, twist angle, and corrugation effect. The biased TBGs exhibit unusual plasmonic responses. In the long-wavelength limit, the plasmon frequency is nearly independent of the carrier density but can be tuned by the bias voltage.