Abstract
We study the scattering problem for a two-dimensional perturbed Dirac operator in a strip, corresponding to an electron on the surface of a strong three-dimensional topological insulator. We consider the possibility of electron spin polarization and investigate the transmission probability for the ferromagnetic/normal/ferromagnetic and normal/barrier/normal junctions. For the case of a small potential and low velocities of the incident electron, and for some other cases, we obtain simple formulas for the transmission probability.
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