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.
Highlights
Topological materials such as topological insulators [1], transition metal dichalcogenides [2] andWeyl and Dirac semimetals [3,4,5] have opened a new and active branch of condensed matter physics with considerable potential for spin electronics, thermoelectricity, magnetoelectronics and topological quantum computing [6]
We focus on two prototype systems: (i) topological insulators as representing massless Dirac fermions and (ii) Dirac/Weyl semimetal thin films as representing massive Dirac fermions
On a qualitative level, it is natural to expect that extrinsic spin-orbit coupling terms will play an important role in weak localization (WL)/weak antilocalization (WAL) in transition metal dichalcogenides, and, due to the same non-commutativity of spin matrices we have identified, we expect terms linear in the extrinsic spin-orbit coupling to be present in WL/WAL in these materials
Summary
Topological materials such as topological insulators [1], transition metal dichalcogenides [2] and. The diffusion constant, which is linear in the strength of the disorder spin-orbit coupling as opposed to the quadratic dependence observed for a parabolic dispersion This term appears in the Bloch lifetime of the quasiparticles, the transport relaxation time, the spin relaxation time, and the Cooperon, and gives rise to a non-trivial density dependence of the quantum correction to the conductivity, which may be observable when the quasiparticle mass is very small, namely in topological insulators. They key point part of our analysis is provided by Equations (15) and (16) below, which are completely general and can be used to fit WL/WAL experiments on both massless and massive Dirac fermions.
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