Scattering of two-dimensional massless Dirac electrons by a circular potential barrier

Jhih Sheng Wu, Michael M. Fogler

Research output: Contribution to journalArticle

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Abstract

We calculate the differential, total, and transport cross-sections for scattering of two-dimensional massless Dirac electrons by a circular barrier. For scatterer of a small radius, the cross-sections are dominated by quantum effects such as resonant scattering that can be computed using the partial-wave series. Scattering by larger size barriers is better described within the classical picture of reflection and refraction of rays, which leads to phenomena of caustics, rainbow, and critical scattering. Refraction can be negative if the potential of the scatterer is repulsive, so that a p-n junction forms at its boundary. Qualitative differences of this case from the n-N doping case are examined. Quantum interference effects beyond the classical ray picture are also considered, such as normal and anomalous diffraction, and also whispering-gallery resonances. Implications of these results for transport and scanned-probe experiments in graphene and topological insulators are discussed.

Original languageEnglish
Article number235402
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume90
Issue number23
DOIs
StatePublished - 1 Dec 2014

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