Angular dependence of negative magneto resistance in the Weyl semimetals

Three dimensional Weyl semimetals have recently been
observed to have negative magnetoresistance
with the magnetic field parallel to the electric field
and positive magnetoresistance with the magnetic field perpendicular
to the electric field.
It is understood that the negative magnetoresistance is due to a Berry
phase that causes the chiral anomaly,
while the positive magnetoresistnce can be understood in terms of
conventional semiclassical transport theory.
We solve the semiclassical Boltzmann equation with both the
Berry phase and Lorentz force terms present for an arbitrary angle
of the applied magnetic field relative to the electric field
within the relaxation time approximation.
The low field magnetoresistance does change from negative to positive
as one rotates the magnetic field away from the direction of the
electric field. As the magnetic field is increased we find in some
cases the magnetoresistance starts out negative and then become positive.
This is consistent with recent experimental data in $Cd_{3}As_{2}$.