Less is more: Vacancy-engineered interacting nodal-line semimetals

We show that lattice engineering with certain periodic distributions of vacancies yields a novel type of nodal-line semimetal which possess symmetry-enforced nodal lines, which are immune to arbitrarily large symmetry-preserving perturbations, and unusually robust accidental nodal lines. Both types of nodal lines arise from the structural features of the proposed vacancy-engineered lattices, as demonstrated using a minimal effective model and verified by first-principles calculations of vacancy-engineered graphene and borophene sheets. The effect of electron-electron (e-e) interaction in vacancy-engineered graphene is addressed by quantum Monte Carlo simulations. Former studies of the pristine honeycomb lattice have demonstrated the occurrence of a quantum phase transition from a metallic to an insulating antiferromagnetic phase at a critical strength of the e-e interaction. We investigate if a long-range magnetic order exists in vacancy-engineered graphene and, if so, what type of magnetic order and the relation between the existence of nodal lines in the single-particle spectrum and the onset of the magnetic order in the interacting case.