TY - JOUR

T1 - Scattering of two-dimensional massless Dirac electrons by a circular potential barrier

AU - Wu, Jhih Sheng

AU - Fogler, Michael M.

PY - 2014/12/1

Y1 - 2014/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84916214667&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.90.235402

DO - 10.1103/PhysRevB.90.235402

M3 - Article

AN - SCOPUS:84916214667

VL - 90

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

SN - 1098-0121

IS - 23

M1 - 235402

ER -