Filling-enforced Dirac loops and their evolutions under various perturbations.

Based on symmetry analysis, we propose that filling-enforced Dirac loops (FEDLs) in non-magnetic systems exist and only exist in only five space groups (SGs), namely, SG.57, SG.60, SG.61, SG.62 and SG.205. %, respectively. We explore all possible configurations of the FEDLs in these space groups, and classify them accordingly. Furthermore, we study the evolutions of the FEDLs under various types of symmetry-breaking perturbations, such as an applied strain or an external field. The results show that FEDL materials can serve as parent materials of both topological semimetals hosting nodal points/loops, and topological insulators/topological crystalline insulators. By means of first-principles calculations, many materials possessing FEDLs are predicted.