Two-dimensional Dirac nodal-line semimetal against strong spin-orbit coupling in real materials

Symmetry is one of the conceptual pillars underlying fundamental understanding of electronic band structures of materials. Unique symmetries have boosts continuous discoveries of Dirac materials with intriguing electronic phases in the past decade. A long-standing challenge in the community lies in searching for robust Dirac nodal line semimetals (DNLSs) in two-dimensional (2D) systems where the low-energy fermionic excitations along the four-fold degenerate Dirac nodal line (DNL) would essentially dominate the electrical properties of the 2D materials. However, such four-fold degenerate lines are usually vulnerable to spin-orbit coupling (SOC). A real 2D DNLS material, that shows robustness to SOC, is yet to be experimentally discovered or proved. Here, by combing molecular beam epitaxy growth on black phosphorus substrates (BP), scanning tunneling microscopy (STM) characterization, density functional theory (DFT) calculations and space group theory analysis, we reveal a solely symmetry dictated SOC-robust DNL in real 2D crystalline structures. A tri-atomic layers bismuth (3-ALs Bi) exhibits a unique structure, defining a non-symmorphic space group 1) protecting the four-fold degeneracy of the nodal line no matter SOC is present or not; 2) introducing linear dispersion relations at the vicinity of the nodal line. This guarantees the robust DNL electronic phase without any orbital and element dependence. With this inherent relation, we expect and theoretically prove the generality of the robust DNL in a series of 2D layers that are isostructural to 3-ALs Bi. This opens the door towards growth, exploration and utilization of intrinsic 2D DNL materials. In the 3-ALs Bi case, the DNL state is near the Fermi level (EF) and is rather neat that other trivial bands open a gap around the EF, making the 3-ALs Bi one of the ``cleanest" DNL semimetal (DNLSs) ever proposed.