Robust Topological Nodal-Line Semimetals from Periodic Vacancies in Two-Dimensional Materials

A nodal-line semimetal (NLSM) is suppressed in the presence of spin–orbit coupling unless it is protected by a nonsymmorphic symmetry. We show that two-dimensional (2D) materials can realize robust NLSMs when vacancies are introduced on the lattice. As a case study we investigate borophene, a boron honeycomb-like sheet. While the Dirac cones of pristine borophene are shown to be gapped out by spin–orbit coupling and by magnetic exchange, robust nodal lines (NLs) emerge in the spectrum when selected atoms are removed. We propose an effective 2D model and a symmetry analysis to demonstrate that these NLs are topological and protected by a nonsymmorphic glide plane. Our findings offer a paradigm shift to the design of NLSMs: instead of searching for nonsymmorphic materials, robust NLSMs may be realized simply by removing atoms from ordinary symmorphic crystals.