  Recently, a new type of Weyl semimetal called type-II Weyl semimetal has been
proposed. Unlike the usual (type-I) Weyl semimetal, which has a point-like
Fermi surface, this new type of Weyl semimetal has a tilted conical spectrum
around the Weyl point. Here we calculate the anomalous Hall conductivity of a
Weyl semimetal with a tilted conical spectrum for a pair of Weyl points, using
the Kubo formula. We find that the Hall conductivity is not universal and can
change sign as a function of the parameters quantifying the tilts. Our results
suggest that even for the case where the separation between the Weyl points
vanishes, tilting of the conical spectrum could give rise to a finite anomalous
Hall effect, if the tilts of the two cones are not identical.
