The Kondo effect in three-dimensional topological insulators

Abstract

We investigate the role of magnetic impurities in the transport properties of surface states on a three-dimensional topological insulator. First, we use second-order perturbation theory and the Boltzmann transport equation to calculate the magnetically induced resistivity in a topological insulator. Our result shows a non-perturbative behavior when conducting electrons and magnetic impurities' spins are antiferromagnetically coupled. The surface resistivity is found to display an oscillatory rather than isotropic behavior compared to the conventional Kondo effect. Both the variational method and renormalization group (RG) analysis are employed to compute the Kondo temperature, through which the non-perturbative behavior is confirmed. We further study the RG flows and demonstrate that the RG trajectories flow into a strong coupling regime if coupling is antiferromagnetic. Our work is motivated by the recent transport experiments with surface currents on topological insulators. Our calculation is qualitatively consistent with the low temperature dip observed in the experimental R-T curve and might be one of the possible origins of the dip.

Magnetotransport measurements of the surface states of samarium hexaboride using Corbino structures

“…On both surfaces, as the temperature is reduced, we observe a logarithmic increase of the resistance, the coefficient of which is far from the quantum conductance e 2 /h. This, taken together with the low-field increase in µ(B), suggests a TI surface Kondo scattering mechanism 33,34 . We expect that there are significant magnetic impurities on the SmB 6 surface, based on recent X-ray magnetic circular dichroism and X-ray absorption spectroscopy spectra which show that Sm 3+ with a net magnetic moment is dominant on the surface 35 .…”

“…The logarithmic T -dependence of the electron scattering rate we observe can be fit using the following formula 34 , developed for a 3D TI system with dilute magnetic impurities:…”

Influence of helical spin structure on the magnetoresistance of an ideal topological insulator

“…Even for the simplified mean-field approach, a single magnetic impurity additionally deforms the helical spin angles, which have only been calculated numerically [32]. Spin-flip scattering by magnetic impurities, which gives rise to the Kondo effect, can be even more demanding theoretically [33].…”

Tunable unconventional Kondo effect on topological insulator surfaces

“…When this field is large enough the spin degree of freedom of conduction electrons is effectively lost and cannot participate in the spin-flip scattering leading to the Kondo effect. Nevertheless there is substantial theoretical evidence 26,[30][31][32][33][34] indicating that a magnetic impurity on a TI surface is screened by the surface metal. Remarkably the physical nature of this effect and spatial structure of the screening states have never been elucidated in the context of TIs.…”