Spinless hourglass nodal-line semimetals

Understand

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.