Theory of multiple magnetic scattering for quasiparticles on a gapless topological insulator surface
Zhen-Guo Fu, Ping Zhang, Zhigang Wang, Fawei Zheng, Shu-Shen Li
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.