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

TL;DR

This paper investigates magnetic impurities on topological insulator surfaces, revealing that their Kondo effect mirrors graphene, and explores how magnetic fields influence Friedel oscillations and local density of states, highlighting unique spin-locking physics.

Contribution

It demonstrates the equivalence of the Kondo effect on topological insulator surfaces and graphene, and analyzes magnetic field effects on Friedel oscillations and impurity states.

Findings

Kondo effect on topological insulator surfaces is similar to graphene.

Magnetic field alters Friedel oscillation patterns from inverse-square to inverse behavior.

Peak splitting in local density of states does not follow linear magnetic field dependence.

Abstract

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. Third, we examine the Friedel oscillation around the magnetic impurity. It turns out that the pattern of Friedel oscillation in the helical surface is identical to that of the graphene surface, displaying the inverse-square behavior $\sim r^{-2}$ if the inter-valley scattering is not introduced in the graphene case. However, introduction of the magnetic field leads the electron density of states from the inverse-square physics to the inverse behavior $\sim r^{-1}$ in the topological insulator's surface while it still remains as $\sim r^{-2}$ in the graphene Kondo effect. We discuss that this originates from spin flipping induced by magnetic field.