  We show that, under the effect of an external magnetic field, a photogalvanic
effect and the generation of second harmonic wave can be induced in
inversion-symmetric and time reversal invariant Dirac semimetals. The mechanism
responsible of these non linear optical responses is the magnetochiral effect.
The origin of this magnetochiral effect is the band bending of the dispersion
relation in real Dirac semimetals. Some observable consequences of this
phenomenon are the appearance of a dc current on the surface of the system when
it is irradiated with linearly polarized light or a rotation of the
polarization plane of the reflected second harmonic wave.
