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.