  Weyl semimetals are three-dimensional topological states of matter, in a
sense that they host paired monopoles and antimonopoles of Berry curvature in
momentum space, leading to the chiral anomaly. The chiral anomaly has long been
believed to give a positive magnetoconductivity or negative magnetoresistivity
in strong and parallel fields. However, several recent experiments on both Weyl
and Dirac topological semimetals show a negative magnetoconductivity in high
fields. Here, we study the magnetoconductivity of Weyl and Dirac semimetals in
the presence of short-range scattering potentials. In a strong magnetic field
applied along the direction that connects two Weyl nodes, we find that the
conductivity along the field direction is determined by the Fermi velocity,
instead of by the Landau degeneracy. We identify three scenarios in which the
high-field magnetoconductivity is negative. Our findings show that the
high-field positive magnetoconductivity may not be a compelling signature of
the chiral anomaly and will be helpful for interpreting the inconsistency in
the recent experiments and earlier theories.
