Weak Localization and Antilocalization in Topological Materials with Impurity Spin-Orbit Interactions

Abstract

Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglected. In this work, we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions in Weyl semimetal thin films, taking into account both intrinsic and extrinsic spin-orbit interactions. The physics is governed by the complex interplay of the chiral spin texture, quasiparticle mass, and scalar and spin-orbit scattering. We demonstrate that terms linear in the extrinsic spin-orbit scattering are generally present in the Bloch and momentum relaxation times in all topological materials, and the correction to the diffusion constant is linear in the strength of the extrinsic spin-orbit. In topological insulators, which have zero quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to an observable density dependence in the weak antilocalization correction. They produce substantial qualitative modifications to the magnetoconductivity, differing greatly from the conventional Hikami-Larkin-Nagaoka formula traditionally used in experimental fits, which predicts a crossover from weak localization to antilocalization as a function of the extrinsic spin-orbit strength. In contrast, our analysis reveals that topological insulators always exhibit weak antilocalization. In Weyl semimetal thin films having intermediate to large values of the quasiparticle mass, we show that extrinsic spin-orbit scattering strongly affects the boundary of the weak localization to antilocalization transition. We produce a complete phase diagram for this transition as a function of the mass and spin-orbit scattering strength. Throughout the paper, we discuss implications for experimental work, and, at the end, we provide a brief comparison with transition metal dichalcogenides.

Formation of Surface and Quantum-Well States in Ultra Thin Pt Films on the Au(111) Surface

“…The energy separation between these two sets of bands at is about 0.6 eV in the SOC calculation and comparable with energy splitting of a double-degenerate band I along the direction of the bulk Brillouin zone of Figure 3 b. Each pair of these bands is degenerate only at the point and its dispersion has shape of a Dirac cone similar to that realized in the topological materials [ 101 , 102 , 103 , 104 ]. These four energy bands continue to be true electronic states inside the Au(111) s - p energy gap.…”

Two-dimensional superconductivity and magnetotransport from topological surface states in AuSn4 semimetal

“…One can see that parameter a is negative due to a positive magnetoresistance and at higher temperatures; the decrease in |a| values with an increase in temperature indicates a gradual absence of the WAL effect on the field-dependent transverse magnetoconductivity. It is known that in topological materials, strong spin-orbit coupling can induce WAL 53 , and this WAL effect originates from the strong spin-orbit coupling in the band structure, and results in the spinmomentum locking in the topological surface states 54 . Therefore, the WAL phenomenon is always observed in topological materials as an important consequence of spin-momentum locking, as well as the full suppression of backscattering, which is a fingerprint of the surface states 55 .…”

Energy spectrum, the spin polarization, and the optical selection rules of the Kronig-Penney superlattice model with spin-orbit coupling

“…Semiconductor materials with strong spin-orbit coupling (SOC) have attracted considerable interest in recent years because of their potential applications in both condensed-matter physics and quantum-information processing [1][2][3]. For example, a topological insulator phase has been discovered in strong spin-orbit coupled quantum-well structures [4], and a strong spin-orbit coupled semiconductor nanowire in proximity to a s-wave superconductor can realize an 1D topological superconductor [5,6].…”