Probing surface states of topological insulator: Kondo effect and Friedel oscillation under magnetic field

Understand

We address three issues on the role of magnetic impurities in the surface state of a three dimensional topological insulator.

• First, we prove that the Kondo effect of the topological surface is essentially the same as that of the graphene surface, demonstrating that an effective impurity action of the topological surface coincides with that of the graphene surface.
• Second, we study the role of the $z$-directional magnetic field ($h$) in the Kondo effect, and show that the peak splitting in the impurity local density of states does not follow the $h$-linear behavior, the typical physics in the soft-gap Kondo model.
• We discuss that the origin is spin locking in the helical surface.