  Non-symmorphic symmetries protect Dirac nodal lines and cones in lattice
systems. Here, we investigate the spectral properties of a two-dimensional
lattice belonging to a non-symmorphic group. Specifically, we look at the
herringbone lattice, characterised by two sets of glide symmetries applied in
two orthogonal directions. We describe the system using a nearest-neighbour
tight-binding model containing horizontal and vertical hopping terms. We find
two non-equivalent Dirac cones inside the first Brillouin zone along a
high-symmetry path. We tune these Dirac cones' positions by breaking the
lattice symmetries using onsite potentials. These Dirac cones can merge into a
semi-Dirac cone or unfold along a high-symmetry path. Finally, we perturb the
system by applying a dimerization of the hopping terms. We report a flow of
Dirac cones inside the first Brillouin zone describing quasi-hyperbolic curves.
We present an implementation in terms of CO atoms placed on the top of a
Cu(111) surface.
