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