PT-invariant Weyl semimetals in gauge-symmetric systems

Weyl semimetals typically appear in systems in which either time-reversal (T) or inversion (P) symmetry is broken. Here we show that in the presence of gauge potentials these topological states of matter can also arise in fermionic lattices preserving both T and P. We analyze in detail the case of a cubic lattice model with pi fluxes, discussing the role of gauge symmetries in the formation of Weyl points and the difference between the physical and the canonical T and P symmetries. We examine the robustness of this PT-invariant Weyl semimetal phase against perturbations that remove the chiral sublattice symmetries, and we discuss further generalizations. Finally, motivated by advances in ultracold-atom experiments and by the possibility of using synthetic magnetic fields, we study the effect of random perturbations of the magnetic fluxes, which can be compared to a local disorder in realistic scenarios.