Berlin 2015 – scientific programme

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O: Fachverband Oberflächenphysik

O 28: Moire and Graphene Stacking

O 28.2: Talk

Tuesday, March 17, 2015, 14:15–14:30, MA 041

Semi-classical method for matrix valued Hamiltonians — •Michael Vogl, Sam Shallcross, and Oleg Pankratov — Lehrstuhl für Theoretische Festkörperphysik Staudtstr. 7-B2 91058 Erlangen

Semi-classical theories are interesting for their insight into the borderland phenomena embracing quantum and classical physics such as quantum chaos, as well as for providing a non-perturbative scheme for treating complex quantum problems. The plethora of complex graphene-based systems, such as the twist graphene bilayer consisting of two mutually rotated carbon layers, or the AB stacked bilayer with soliton faults (partial dislocations), are systems for which a semi-classical treatment should be very useful. However, the usual semi-classical schemes become prohibitively cumbersome for the matrix valued Hamiltonians inherent to the graphene-based systems. We provide a scheme that allows for a clear route to the semi-classical treatment of such systems, as well as a very efficient numerical scheme.[1] As an example of this procedure we consider the semi-classical treatment of a line partial dislocation in bilayer graphene.

[1] M. Vogl, Semi-classics for Matrix Hamiltonians, Master thesis, Erlangen, 2014.