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

We develop a general low-energy multiple-scattering partial-wave theory for gapless topological insulator surfaces in the presence of magnetic impurities. As applications, we discuss the differential cross section (CS) dΛ/dφ, the total CS Λ _tot, the Hall component of resistivity Ω, and inverse momentum relaxation time Γ _M for single- and two-centered magnetic scattering. We show that differing from the nonmagnetic impurity scattering, s-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 nonzero perpendicular resistivity component Ω, which may be useful for tuning the Hall voltage of the sample. Consistent with the analysis of dΛ/dφ, by comparing Γ _M with Λ _tot, we can determine different weights of backscattering and forward scattering. Similar to CS, Ω and Γ _M also exhibit oscillating behavior for multiple-magnetic- scattering centers due to interference effect.