Tunable topological Weyl semimetal from simple-cubic lattices with staggered fluxes

Three-dimensional Weyl fermions are found to emerge from simple-cubic lattices with staggered fluxes. The mechanism is a gapping of the quadratic-band touching by time-reversal-symmetry-breaking hoppings. The system exhibits a rich phase diagram where the number of Weyl fermions and their topological charges are tunable via plaquette fluxes. The Weyl semimetal state is shown to be the intermediate phase between a nontopological semimetal and a 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 of 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.