Berlin 2015 – scientific programme

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O: Fachverband Oberflächenphysik

O 28: Moire and Graphene Stacking

O 28.4: Talk

Tuesday, March 17, 2015, 14:45–15:00, MA 041

Low energy theory of the graphene twist bilayer — •Dominik Weckbecker, Sam Shallcross, and Oleg Pankratov — Lehrstuhl für Theoretische Festkörperphysik, Staudtstraße 7, D-91058 Erlangen, Germany

Two mutually rotated layers of graphene exhibit an electronic structure that depends profoundly on the rotation angle of the two layers. At large angles the layers essentially decouple while, in contrast, for small rotation angles strong coupling leads to a dramatically different electronic spectrum: one finds localization on the moire lattice and a significant reduction of the Fermi velocity near the Dirac point [1]. This richness of electronic structure has however proven difficult to capture within an unified low energy Dirac-Weyl picture; while theories exist for the large and small angle regimes there is at present no consistent theory valid at all twist angles [2,3]. We remedy this by deriving a low energy theory which is based on the observation of an emergent momentum coupling scale [1] valid at all angles, which we show to be in excellent agreement with numerical tight-binding calculations. We further explore the rich small angle limit finding a vanishing of the zero mode and a rich gallery of Fermi surfaces. At large angles the theory recovers the effective low energy Hamiltonians previously derived on symmetry grounds [3].

[1] S. Shallcross et al., Phys. Rev. B 87, 245403, 2013.

[2] R. Bistritzer et al., PNAS 108(30):12233-12237, 2011.

[3] E. J. Mele et al., J. Phys. D: Appl. Phys. 45 154004, 2012.