  Using first-principles calculations, we investigate the photogalvanic effect
in the Weyl semimetal material TaAs. We find colossal photocurrents caused by
the Weyl points in the band structuure in a wide range of laser frequency. Our
calculations reveal that the photocurrent is predominantly contributed by the
three-band transition from the occupied Weyl band to the empty Weyl band via an
intermediate band away from the Weyl cone, for excitations both by linearly and
circularly polarized lights. Therefore, it is significant to sum over all
three-band transitions by considering a full set of Bloch bands (both Weyl
bands and trivial bands) in the first-principles band structure while it does
not suffice to only consider the two-band direct transition within a Weyl cone.
Calculated photoconductivities are well consistent with recent experiment
measurements. Our work provides the first first-principles calculation on
nonlinear optical phenomena of Weyl semimetals and serves as a deep
understanding of the photogalvanic effects in complexed materials.
