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Scattering of Dirac electrons by circular mass barriers: valley filter and resonant scattering

The scattering of two-dimensional (2D) massless Dirac electrons is investigated in the presence of a random array of circular mass barriers. The inverse momentum relaxation time and the Hall factor are calculated and used to obtain parallel and perpendicular resistivity components within linear transport theory. We found a non zero perpendicular resistivity component which has opposite sign for electrons in the different K and K' valleys. This property can be used for valley filter purposes. The total cross-section for scattering on penetrable barriers exhibit resonances due to the presence of quasi-bound states in the barriers that show up as sharp gaps in the cross-section while for Schrödinger electrons they appear as peaks.