  A new class of photocurrents is predicted to occur in both type-I and type-II
Weyl semimetals. Unlike the previously studied photocurrents in chiral
materials, the proposed current requires neither circularly polarized light,
nor an absence of symmetry with respect to a plane of reflection. We show that
if a Weyl semimetal has a broken inversion symmetry then linearly polarized
light can induce a photocurrent transverse to the direction of an applied
magnetic field, in spite of the symmetry with respect to a reflection plane and
the time reversal symmetry. The class of materials in which we expect this to
occur is sufficiently broad and includes the transition metal monopnictides
such as TaAs. The effect stems from the dynamics of Weyl chiral quasi-particles
in a magnetic field, restricted by the symmetries described above; because the
resulting current is transverse to the direction of magnetic field, we call it
the transverse chiral magnetic photocurrent. The magnitude of the resulting
photocurrent is predicted to be significant in the THz frequency range, about
$0.75\; \mathrm{\mu A}$ for type-I and $2.5\; \mathrm{\mu A}$ for type-II Weyl
semimetals. This opens the possibility to utilize the predicted transverse
chiral magnetic photocurrent for sensing unpolarized THz radiation.
