  Three-dimensional Weyl fermions are found to emerge from simple cubic
lattices with staggered fluxes. The mechanism is to gap the quadratic band
touching by time-reversal-symmetry-breaking hoppings. The system exhibits rich
phase diagrams where the number of Weyl fermions and their topological charge
are tunable via the plaquette fluxes. The Weyl semimetal state is shown to be
the intermediate phase between non-topological semimetal and quantum anomalous
Hall insulator. The transitions between those phases can be understood through
the evolution of the Weyl points as Berry flux insertion processes. As the Weyl
points move and split (or merge) through tuning the plaquette fluxes, the Fermi
arcs and surface states undergo significant manipulation. We also propose a
possible scheme to realize the model in ultracold fermions in optical lattices
with artificial gauge fields.
