WKB analysis of edge states in graphene in a strong magnetic field

Abstract

We investigate the fine structure of the edge states energy spectrum for zigzag and armchair ribbons of graphene in a strong magnetic field. At low energy, the spectra can be described by an effective Schrodinger Hamiltonian with a double well potential, symmetric in the zigzag case and asymmetric in the armchair case. We develop a semiclassical formalism based on the WKB approximation to calculate analytically the energy spectrum for the two types of edges, including regions which were not studied earlier. Our results are in very good quantitative agreement with numerical calculations. This approach leads to a qualitative description of the spectra in terms of the quantization of unusual classical orbits in the real space.

arXiv comment20 pages, 25 figures

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• Transparent Graphene-Superconductor Interfaces: Quantum Hall and Zero Field Regimes
• Zigzag edge states in graphene in the presence of in-plane electric field
• Developing a semiclassical Wentzel-Kramers-Brillouin theory for $\alpha -{\mathcal{T}}_3$ model
• Peculiarities of the Landau level collapse in graphene ribbons in crossed magnetic and in-plane electric fields
• Tunable signal velocity in the integer quantum Hall effect of tailored graphene
• Chambers's formula for the graphene and the Hou model with kagome periodicity and applications