Theory of multiple magnetic scattering for quasiparticles on a gapless topological insulator surface

Abstract

We develop a general low-energy multiple-scattering partial-wave theory for gapless topological insulator (TI) surfaces in the presence of magnetic impurities. As applications, we discuss the differential cross section (CS) $d\Lambda/d\varphi$, the total CS $\Lambda_{tot}$, the Hall component of resistivity $\Omega$, and inverse momentum relaxation time $\Gamma_{M}$ for single- and two-centered magnetic scattering. We show that differing from the nonmagnetic impurity scattering, $s\mathtt{-}$wave approximation is not advisable and convergent in the present case. The symmetry of CS is reduced and the backscattering occurs and becomes stronger with increasing the effective magnetic moment $M$ of single magnetic impurity. We show a non-zero perpendicular resistivity component $\Omega$, which may be useful for tuning the Hall voltage of the sample. Consistent with the analysis of $d\Lambda /d\varphi$, by comparing $\Gamma_{M}$ with $\Lambda_{tot}$, we can determine different weights of backscattering and forward scattering. Similar to CS, $\Omega$ and $\Gamma_{M}$ also exhibit oscillating behavior for multiple magnetic scattering centers due to interference effect.