Weyl points on non-orientable Brillouin zones: Nielsen-Ninomiya, Fermi arcs and Z2 topological charge

Weyl fermions are chiral particles in high-energy physics that can also emerge as low-energy quasiparticles near three-dimensional band crossing points. They are subject to the Nielsen--Ninomiya "no-go" theorem when placed on a lattice, requiring their total chirality to vanish. This constraint results from the topology of the (orientable) manifold on which they exist. In this talk, we discuss to what extent the concepts of topology and chirality of Weyl points remain well-defined when the underlying manifold is non-orientable. We show that this setting renders chirality a more subtle concept, as well as allowing for systems with a non-zero net chirality. Furthermore, we discover that Weyl points on non-orientable manifolds carry an additional Z2 invariant, satisfying a similar no-go theorem. We implement such Weyl points by constructing tight-binding models with a momentum-space non-symmorphic symmetry. Finally, we experimentally realize their phenomenology in a photonic platform with synthetic momenta.