PT invariant Weyl semimetals in gauge symmetric systems

Weyl semimetals typically appear in systems in which either time-reversal (T) or inversion (P}) symmetry are 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. Motivated by advances in ultracold atom experiments and by the possibility of using synthetic magnetic fields, we examine the robustness of the Weyl semimetal phase in the presence of trapping potentials and random perturbations of the magnetic fluxes, which can be compared to a local disorder in realistic scenarios.