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Weyl semimetal, a three-dimensional electronic system with relativisticlinear energy dispersion around gapless points carrying nontrivial Berrycharge, is predicted to exhibit a wealth of unique response and transportproperties.A crucial question is whether those properties are robust againstdisorder and whether Anderson localization occurs.In this work, the effects ofnonperturbative topological (vortex loop) excitations and Berry phase indisordered time-reversal invariant 3d Weyl semimetal are studied.It is shownthat the chiral symmetry is restored in the nonlinear sigma model describingthe diffusons upon disorder average as any net topological term and itsdelocalization result do not take effect at sufficiently short lengthscales.Anderson localization occurs at sufficiently strong disorder and wepredict that chirality and related phenomena disappear at suchtransition.Nevertheless, we uncover a mechanism that originates from Berryphase that impedes such localization effect.We show the occurrence ofdestructive interference between the vortex loops and between scattering pathsdue to the the vortex loops' Berry phase which resists the Andersonlocalization.We emphasize the applicability of our theory to the candidate Weylmaterials where we point out the consistency of our theory with a recentexperimental finding of the absent chiral anomaly in a noncentrosymmetric Weylsemimetal.

On Anderson Localization and Chiral Anomaly in Disordered Time-Reversal Invariant Weyl Semimetals: Nonperturbative and Berry Phase Effects