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

TL;DR

This paper develops a comprehensive low-energy multiple-scattering theory for magnetic impurities on gapless topological insulator surfaces, revealing unique scattering behaviors, resistivity components, and interference effects.

Contribution

It introduces a novel partial-wave multiple-scattering framework for magnetic impurities on TI surfaces, highlighting the failure of s-wave approximation and the impact of magnetic moments.

Findings

Backscattering increases with magnetic moment M.

Perpendicular resistivity component Omega can be tuned via magnetic impurities.

Interference effects cause oscillations in scattering and resistivity metrics.

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.