First-principles study on symmetry-protected Dirac nodal lines in a square net material CaZnBi₂

We investigate the atomic and electronic structures of AZnBi2 (A = Ca, Sr, Ba) family of material using first-principles density functional theory. The material class shows interesting band structures around the Fermi energy, mainly derived from the Bi-square net. Moreover, as the A-site cation radius increases, the space group of the ground-state atomic structure changes from P4/nmm to I4/mmm space group, with associated changes in the A-site coordination around the Bi square net. Focusing on the evolution of the band structures due to the change in A-site coordination, we find that in the absence of spin-orbit coupling, either Dirac point or nodal line structures emerge along the Γ-M high symmetry line, which in turn are gapped by spin-orbit coupling. In contrast, the degeneracy at the X-point is protected by the non-symmorphic symmetry of the P4/nmm structure, even in the presence of the spin-orbit coupling, enforcing the semimetal phase. Our work shows the role of the symmetry that dictates the band crossings around the Fermi energy and protects the metallic phase for the P4/nmm structure with non-symmorphic symmetry, which is determined by the A-site coordination around the Bi square net.