  We develop a theory of circular photogalvanic effect in non-gyrotropic
two-dimensional transition metal dichalcogenide monolayers under interband
optical transitions. Oblique incidence of circularly-polarized electromagnetic
field or normal incidence of elliptically polarized electromagnetic field is
assumed. In contrast to the linear-in-intensity conventional photogalvanic
effect, the effect considered here arises in the second intensity order. The
effect is conditioned by i) the predominant population of the valleys by the
circular in-plane electromagnetic field component and ii) the direct drift of
the photo-excited carriers by the linear-polarized in-plane electromagnetic
field component in the presence of trigonal valley asymmetry.
