Magnetic scattering of Dirac fermions in topological insulators and graphene

We study quantum transport and scattering of massless Dirac fermions by spatially localized static magnetic fields. The employed model describes in a unified manner the effects of orbital magnetic fields, Zeeman and exchange fields in topological insulators, and the pseudo-magnetic fields caused by strain or defects in monolayer graphene. The general scattering theory is formulated, and for radially symmetric fields, the scattering amplitude and the total and transport cross sections are expressed in terms of phase shifts. As applications, we study ring-shaped magnetic fields (including the Aharanov-Bohm geometry) and scattering by magnetic dipoles.