Dresden 2014 – wissenschaftliches Programm

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O: Fachverband Oberflächenphysik

O 36: Posters: Bio/organic Molecules on Surfaces, Graphene, Solid/liquid interfaces, Metal Substrates, Electronic Structure Theory

O 36.99: Poster

Dienstag, 1. April 2014, 18:30–22:00, P1

Semiclassics for matrix Hamiltonians and semiclassical perturbation theory and its use for graphene physics — •Michael Vogl, Sam Shallcross, and Oleg Pankratov — Lehrstuhl für Theoretische Festkörperphysik Staudtstr. 7-B2 91058 Erlangen

Electrons in graphene based systems are for low energies often described very well by first quantized matrix Hamiltonians, such as the Dirac-Weyl Hamiltonian in the case of single layer graphene. Nevertheless, such Hamiltonians remain, especially for the more complex graphene multilayer systems such as the twist graphene bilayer, very difficult to solve. Semi-classical methods often give great insight into the underlying structure of such complex systems; in particular in terms of semi-classical orbits and 2-forms such as the Berry phase. Following Bolte and Keppeler [1] we derive a general semi-classical method for treating the matrix Hamiltonians that arise in graphene based systems. This is based on an ansatz for the time-dependent Greens function that allows one to effectively bypass the problems of solution matching that, in other approaches, severly curtails the efficiency of the semi-classical approach. This leads, for a n× n Hamiltonian, to n Hamilton-Jacobi equations, and n transport equations. From the latter arises a term that can be separated into a term resembling the Berry phase and a term arising from the coupling between the n classical systems. We implement this scheme for the Bernal bilayer modeled by the full 4×4 Hamiltonian, as well as exploring how the theory may be implemented for the more complex case of the graphene twist bilayer. [1]J. Bolte & S. Keppeler Phys. Rev. Lett. 81 (1998) 1987-1991