  Torsion can be realized as dislocation in the crystal lattice of material. It
is particularly interesting if the material has fermions in the spectrum, such
as graphene, topological insulators, Dirac and Weyl semimetals, as it's
transport properties can be affected by the torsion. In this paper, we find
that, due to Weyl anomaly, torsion in Dirac and Weyl semimetals can induce
novel chiral currents, either near a boundary or in a ``conformally flat
space''. We briefly discuss how to measure this interesting effect in
experiment. It is remarkable that these experiments can help to clarify the
theoretical controversy of whether an imaginary Pontryagin density could appear
in the Weyl anomaly.
