Magnetic scattering of Dirac fermions in topological insulators and graphene

TL;DR

This paper develops a unified scattering theory for massless Dirac fermions in topological insulators and graphene, analyzing effects of various magnetic fields on quantum transport and scattering phenomena.

Contribution

It introduces a comprehensive scattering framework applicable to different magnetic field configurations affecting Dirac fermions in topological materials.

Findings

Derived phase shift expressions for radially symmetric magnetic fields.

Analyzed scattering in ring-shaped magnetic fields and magnetic dipoles.

Unified treatment of orbital, Zeeman, exchange, and pseudo-magnetic effects.

Abstract

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.