  Negative longitudinal magnetoresistance, in the presence of an external
magnetic field parallel to the direction of an applied current, has recently
been experimentally verified in Weyl semimetals and topological insulators in
the bulk conduction limit. The appearance of negative longitudinal
magnetoresistance in topological semimetals is understood as an effect of
chiral anomaly, whereas it is not well-defined in topological insulators.
Another intriguing phenomenon, planar Hall effect - appearance of a transverse
voltage in the plane of applied co-planar electric and magnetic fields not
perfectly aligned to each other, a configuration in which the conventional Hall
effect vanishes, has recently been suggested to exist in Weyl semimetals. In
this paper we present a quasi-classical theory of planar Hall effect of a
three-dimensional topological insulator in the bulk conduction limit. Starting
from Boltzmann transport equations we derive the expressions for planar Hall
conductivity and longitudinal magnetoconductivity in topological insulators and
show the important roles played by the orbital magnetic moment for the
appearance of planar Hall effect. Our theoretical results predict specific
experimental signatures for topological insulators that can be directly checked
in experiments.
