Less is more: Vacancy-engineered nodal-line semimetals

A nodal-line semimetal phase which is enforced by the symmetries of the material is interesting from fundamental and application standpoints. We demonstrate that such a phase of matter can be engineered by a simple method: Introducing vacancies in certain configurations in common symmorphic materials leads to nonsymmorphic polymorphs with symmetry-enforced nodal lines which are immune to symmetry-preserving perturbations, such as spin-orbit coupling. Furthermore, the spectrum acquires also accidental nodal lines with enhanced robustness to perturbations. These phenomena are explained on the basis of a symmetry analysis of a minimal effective two-dimensional model which captures the relevant symmetries of the proposed structures, and verified by first-principles calculations of vacancy-engineered borophene polymorphs, both with vanishing and with strong Rashba spin-orbit coupling. Our findings offer an alternative path to using complicated nonsymmorphic compounds to design robust nodal-line semimetals; one can instead remove atoms from a simple symmorphic monoatomic material.