Title: Spinless hourglass nodal-line semimetals,
Abstract: Nodal-line semimetals, one of the topological semimetals, have degeneracy
along nodal lines where the band gap is closed. In many cases, the nodal lines
appear accidentally, and in such cases it is impossible to determine whether
the nodal lines appear or not, only from the crystal symmetry and the electron
filling. In this paper, for spinless systems, we show that in specific space
groups at $4N+2$ fillings ($8N+4$ fillings including the spin degree of
freedom), presence of the nodal lines is required regardless of the details of
the systems. Here, the spinless systems refer to crystals where the spin-orbit
coupling is negligible and the spin degree of freedom can be omitted because of
the SU(2) spin degeneracy. In this case the shape of the band structure around
these nodal lines is like an hourglass, and we call this a spinless hourglass
nodal-line semimetal. We construct a model Hamiltonian as an example and we
show that it is always in the spinless hourglass nodal-line semimetal phase
even when the model parameters are changed without changing the symmetries of
the system. We also establish a list of all the centrosymmetric space groups,
under which spinless systems always have hourglass nodal lines, and illustrate
where the nodal lines are located. We propose that Al$_3$FeSi$_2$, whose
space-group symmetry is Pbcn (No. 60), is one of the nodal-line semimetals
arising from this mechanism.