Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2010-05-28
Physica Status Solidi (b), 247, 2949-2952 (2010)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
4 pages, 5 figures This manuscript should be published in the proceedings volume of the conference IWEPNM 2010, in the Physica
Scientific paper
10.1002/pssb.201000160
We theoretically study the scattering of a plane wave of a ballistic electron on a circular n-p junction in single and bilayer graphene. We compare the exact wave function inside the junction to that obtained from a semiclassical formula developed in catastrophe optics. In the semiclassical picture short-wavelength electrons are treated as rays of particles that can get reflected and refracted at the n-p junction according to Snell's law with negative refraction index. We show that for short wavelength and close to caustics this semiclassical approximation gives good agreement with the exact results in the case of single-layer graphene. We also verify the universal scaling laws that govern the shrinking rate and intensity divergence of caustics in the semiclassical limit. It is straightforward to generalize our semiclassical method to more complex geometries, offering a way to efficiently design and model graphene-based electron-optical systems.
Cserti József
Koltai János
Pályi András
Péterfalvi Csaba
Rusznyák Ádám
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