Symmetry and non-Hermiticity play pivotal roles in photonic lattices. While
symmetries such as parity-time (PT) symmetry have attracted ample
attention, more intricate crystalline symmetries have been neglected in
comparison.
Here, we investigate the impact of the 17 wallpaper space groups of
two-dimensional crystals on non-Hermitian band structures. We show that the
non-trivial space group representations enforce degeneracies at high symmetry
points and dictate their dispersion away from these points. In combination with
either T or PT, the symmorphic p4mm symmetry, as well
as the non-symmorphic p2mg, p2gg, and p4gm symmetries, protect novel
exceptional chains intersecting at the pertinent high symmetry points.Comment: 6 pages, 2 figure