  In condensed matter physics, the term "chiral anomaly" implies the violation
of the separate number conservation laws of Weyl fermions of different
chiralities in the presence of parallel electric and magnetic fields. One
effect of chiral anomaly in the recently discovered Dirac and Weyl semimetals
is a positive longitudinal magnetoconductance (LMC). Here we show that chiral
anomaly and non-trivial Berry curvature effects engender another striking
effect in WSMs, the planar Hall effect (PHE). Remarkably, PHE manifests itself
when the applied current, magnetic field, and the induced transverse "Hall"
voltage all lie in the same plane, precisely in a configuration in which the
conventional Hall effect vanishes. In this work we treat PHE quasi-classically,
and predict specific experimental signatures for type-I and type-II Weyl
semimetals that can be directly checked in experiments.
