  Nonsymmoprhic symmetries, such as screw rotations or glide reflections, can
enforce band crossings within high-symmetry lines or planes of the Brillouin
zone. When these band degeneracies are close to the Fermi energy, they can give
rise to a number of unusual phenomena: e.g., anomalous magnetoelectric
responses, transverse Hall currents, and exotic surface states. In this paper,
we present a comprehensive classification of such nonsymmorphic band crossings
in trigonal materials with strong spin-orbit coupling. We find that in trigonal
systems there are two different types of nonsymmorphic band degeneracies: (i)
Weyl points protected by screw rotations with an accordion-like dispersion, and
(ii) Weyl nodal lines protected by glide reflections. We report a number of
existing materials, where these band crossings are realized near the Fermi
energy. This includes Cu2SrSnS4 and elemental tellurium (Te), which exhibit
accordion Weyl points; and the tellurium-silicon clathrate Te16Si38, which
shows Weyl nodal lines. The ab-initio band structures and surface states of
these materials are studied in detail, and implications for experiments are
briefly discussed.
