  Weyl semimetals are three-dimensional, topologically protected, gapless
phases which show exotic phenomena such as Fermi arc surface states or negative
magnetoresistance. It is an open question whether interparticle interactions
can turn the topological semimetal into a topologically nontrivial Mott
insulating phase. We investigate an experimentally motivated model for Weyl
physics of cold atoms in optical lattices, with the main focus on interaction
effects and topological properties by means of dynamical mean-field theory
(DMFT). We characterize topological phases by numerically evaluating the Chern
number via the Ishsikawa-Matsuyama formula for interacting phases. Within our
studies, we find that the Chern numbers become trivial when interactions lead
to insulating behavior. For a deeper understanding of the
Weyl-semimetal-to-Mott-insulator topological phase transition, we evaluate the
topological properties of quasiparticle bands as well as so-called blind bands.
Our study is complementary to recent studies of Weyl semimetals with DMFT.
