Filling-enforced Dirac nodal loops in the non-magnetic systems and their evolutions under various perturbations

Based on symmetry analysis, we propose that filling-enforced Dirac nodal 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. We explore all possible configurations of the FEDLs in these SGs, 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, almost all materials possessing FEDLs are predicted.