The Kondo effect in three-dimensional topological insulators

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.