  Fracton phase of matter host fractionalized topological quasiparticles with
restricted mobility. A wide variety of fracton models with abelian excitations
had been proposed and extensively studied while the candidates for non-Abelian
fracton phases are less explored. In this work, we investigate the effect of
twisted defect in abelian fracton models. The twisted defect is launched by
introducing a branch cut line hosting anyon condensate. In particular, these
twisted defects, which alter different types of quasiparticles, carry
projective non-Abelian zero modes. En route, such defects can be engineered via
strong onsite hybridization along a branch cut which provides wide tunability
and flexibility in experiment platforms. The braiding of twisted defects with
projective non-Abelian Berry phase renders a new avenue toward fault-tolerant
quantum computation.
