Systematic study of stacked square nets: From Dirac fermions to material realizations

Nonsymmorphic symmetries protect Dirac line nodes in square-net materials. This phenomenon has been most prominently observed in ZrSiS. Here, we systematically study the symmetry-protected nodal fermions that result from different ways of embedding the square net into a larger unit cell. Surprisingly, we find that a nonsymmorphic space group is not a necessary condition for a filling enforced semimetal: symmorphic space groups can also host nodal fermions that are enforced by band folding and electron count, that is, a combination of a particular structural motif combined with electron filling. We apply the results of this symmetry analysis to define an algorithm, which we utilize to find square-net materials with nodal fermions in specific symmorphic space groups. We highlight one result of this search, the compound ThGeSe, which we discuss in the context of nodal fermions. Finally, we discuss how band folding can impose constraints on band connectivity beyond the connectivity of single elementary band representations.