Symmetry guaranteed Dirac-line semimetals in two-dimensions against strong spin-orbit coupling

Abstract: Several intriguing electronic phenomena and electric properties were discovered in three-dimensional Dirac nodal line semimetals (3D-DNLSM), which are, however, easy to be perturbed under strong spin-orbit coupling (SOC). While two-dimensional (2D) layers are an emerging material category with many advantages, 2D-DNLSM against SOC is yet to be uncovered. Here, we report a 2D-DNLSM in odd-atomic-layer Bi (the brick phase, another Bi allotrope), whose robustness against SOC is protected by the little co-group C_2v \times Z^T_2, the unique protecting symmetry we found in 2D.Specially, (4n+2) valence electrons fill the electronic bands in the brick phase, so that the Dirac nodal line with fourfold degeneracy locates across the Fermi level. There are almost no other low energy states close to the Fermi level; this allows to feasibly observe the neat DNLSM-induced phenomena in transport measurements without being affected by other bands. In contrast, Other VA-group elements also form the brick phases, but their DNL states are mixed with the extra states around the Fermi level. This unprecedented category of layered materials allows for exploring nearly isolated 2DDNL states in 2D.