Hourglasslike band structures protected by nonsymmorphic space group symmetries can appear along the high-symmetry lines or on the high-symmetry surfaces of the Brillouin zone. In this work, from symmetry analysis, we demonstrate that $n$-hourglasslike band structures, a generalization of hourglasslike band structures, are enforced along screw-invariant lines in nonmagnetic materials with an $N$-fold screw axis when spin-orbit coupling is finite, where $n$, a nonunity factor of $N$, denotes the degree of the screw-invariant line. The $n$-hourglass has a minimum of $n-1$ crossings, which are Weyl points with monopole charge $\pm 1$. Using compatibility relations, we identify all the space groups that host $n$-hourglasslike band structures induced by screw symmetries, with $n=2,3,4$. For $N=3$ we find Weyl points that are indirectly enforced by symmetries. We construct an effective model, from which we see how the $n$-hourglasses appear when spin-orbit coupling is turned on. As examples, BiPd, the cinnabar phase of HgTe, and the high-temperature phase of ${\mathrm{Tl}}_3{\mathrm{PbBr}}_5$ are shown from first-principles calculations to exhibit $n$-hourglasslike band structures, with $N=2,3,4$, respectively, which confirms our symmetry analysis. For $N=3$ and 4, there are minimally two particle and two hole Fermi pockets enclosing Weyl points at proper fillings, where submanifold nesting may lead to topological density waves.

• Received 31 January 2019
• Revised 12 January 2020
• Accepted 24 February 2020

DOI:https://doi.org/10.1103/PhysRevB.101.115110