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

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.

References added

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Cited by in corpus (9)

• The Physics of Kondo Impurities in Graphene
• Kondo effect on the surface of 3D topological insulators: Signatures in scanning tunneling spectroscopy
• Anomalous Hall response of topological insulators
• Kondo holes in topological Kondo insulators: Spectral properties and surface quasiparticle interference
• Impact of magnetic dopants on magnetic and topological phases in magnetic topological insulators
• Electrically tunable Kondo effect as a direct measurement of the chiral anomaly in disorder Weyl semimetals
• Nambu-Eliashberg theory for multi-scale quantum criticality : Application to ferromagnetic quantum criticality in the surface of three dimensional topological insulators
• Observation of novel interference patterns in Bi2-xFexTe3+d by Fourier transform scanning tunneling spectroscopy
• Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor