  Topological semimetals exhibit band crossings near the Fermi energy, which
are protected by the nontrivial topological character of the wave functions. In
many cases, these topological band degeneracies give rise to exotic surface
states and unusual magneto-transport properties. In this paper, we present a
complete classification of all possible nonsymmorphic band degeneracies in
hexagonal materials with strong spin-orbit coupling. This includes (i) band
crossings protected by conventional nonsymmorphic symmetries, whose partial
translation is within the invariant space of the mirror/rotation symmetry; and
(ii) band crossings protected by off-centered mirror/rotation symmetries, whose
partial translation is orthogonal to the invariant space. Our analysis is based
on (i) the algebraic relations obeyed by the symmetry operators and (ii) the
compatibility relations between irreducible representations at different
high-symmetry points of the Brillouin zone. We identify a number of existing
materials where these nonsymmorphic nodal lines are realized. Based on these
example materials, we examine the surface states that are associated with the
topological band crossings. Implications for experiments and device
applications are briefly discussed.
