Abstract
Weyl semimetal, a three-dimensional electronic system with relativistic linear energy dispersion around gapless points carrying nontrivial Berry charge, is predicted to exhibit a wealth of unique response and transport properties. A crucial question is whether those properties are robust against disorder and whether Anderson localization occurs. In this work, the effects of nonperturbative topological (vortex loop) excitations and Berry phase in disordered time-reversal invariant 3d Weyl semimetal are studied. It is shown that the chiral symmetry is restored in the nonlinear sigma model describing the diffusons upon disorder average as any net topological term and its delocalization result do not take effect at sufficiently short length scales. Anderson localization occurs at sufficiently strong disorder and we predict that chirality and related phenomena disappear at such transition. Nevertheless, we uncover a mechanism that originates from Berry phase that impedes such localization effect. We show the occurrence of destructive interference between the vortex loops and between scattering paths due to the the vortex loops' Berry phase which resists the Anderson localization. We emphasize the applicability of our theory to the candidate Weyl materials where we point out the consistency of our theory with a recent experimental finding of the absent chiral anomaly in a noncentrosymmetric Weyl semimetal.