Filling-enforced Dirac loops and their evolutions under various perturbations

Based on symmetry analysis, we find that filling-enforced Dirac loops (FEDLs) in non-magnetic systems exist in only five space groups. We further explore all possible configurations of these FEDLs in these space groups, and classify them accordingly. We study the evolutions of the FEDLs under various types of perturbations such as applied strain or field. It is interesting that the FEDL-materials can serve as both parent materials of nodal semimetals having Dirac points or nodal-loops, and topological insulators/topological crystalline insulators. Many the FEDL-materials are predicted in DFT calculations.