Berlin 2012 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 22: Graphene: Structure and Theory II

HL 22.4: Talk

Monday, March 26, 2012, 18:00–18:15, EW 201

The Self-similar Limit of the Graphene Twist Bilayer: Zero Mode and Wavefunction Localization — •Sam Shallcross and Oleg Pankratov — Theoretische Festkörperphysik, Universität Erlangen, Staudtstr. 7B2, 91058 Erlangen

The graphene bilayer consisting of mutually rotated layers shows a rich physics, including both a large angle electronic decoupling of the constituent layers, and a small angle regime characterised by an emergent length scale, the moiré length, and dramatic changes in the density of states near the Dirac point [1]. In this work we present tight-binding results for a complete range of twist angles (θ), demonstrating the existance of a small angle limit in which the system becomes self-similar with θ, i.e., reduction of θ leads to no changes in electronic properties when scaled by system size N. This regime is characterised by a zero mode consisting of states strongly localised on the AA patches of the lattice. In addition we present a low energy gauge theory of this self-similar regime, and demonstrate that it yields good agreement with the tight-binding results.

[1] S. Shallcross et al. Phys. Rev. B 81, 165105 (2010)