  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. Here 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
TIs, 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 HLN 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 WSM thin films having intermediate to large
values of the quasiparticle mass 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. We discuss implications for
experiments and provide a brief comparison with transition metal
dichalcogenides.
