  Numerous efforts have been devoted to reveal exotic semimetallic phases with
topologically non-trivial bulk and/or surface states in materials with strong
spin-orbit coupling. In particular, semimetals with nodal line Fermi surface
(FS) exhibit novel properties, and searching for candidate materials becomes an
interesting research direction. Here we provide a generic condition for a
four-fold degenerate nodal line FS in non-symmorphic crystals with inversion
and time-reversal symmetry (TRS). When there are two glide planes or screw axes
perpendicular to each other, a pair of Bloch bands related by non-symmorphic
symmetry become degenerate on a Brillouin Zone (BZ) boundary. There are two
pairs of such bands, and they disperse in a way that the partners of two pairs
are exchanged on other BZ boundaries. This enforces a nodal line FS on a BZ
boundary plane protected by non-symmorphic symmetries. When TRS is broken,
four-fold degenerate Dirac points or Weyl ring FS could occur depending on a
direction of the magnetic field. On a certain surface double helical surface
states exist, which become double Ferm arcs as TRS is broken.
