A systematic study of stacked square nets: from Dirac fermions to material realizations

TL;DR

This paper systematically investigates how different symmetry embeddings of square nets influence the emergence of Dirac fermions, revealing that symmorphic space groups can also host protected nodal fermions due to band folding and electron filling, and applies this to discover new materials like ThGeSe.

Contribution

It introduces a comprehensive symmetry analysis and an algorithm to identify square net materials with nodal fermions in symmorphic space groups, expanding the understanding of symmetry protection mechanisms.

Findings

Symmorphic space groups can host nodal fermions due to band folding and electron filling.

An algorithm was developed to find square net materials with nodal fermions.

ThGeSe is identified as a new material hosting nodal fermions.

Abstract

Non-symmorphic 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 has not been discussed before 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.