3D Analogs of Square-Net Nodal Line Semimetals: Band Topology of Cubic LaIn₃

In two-dimensional (2D) systems, the origins of topological band structure have been linked to simple chemical bonding models. Here, we investigate the three-dimensional (3D) metal LaIn₃ and show that its electronic structure and band topology are well-modeled using a tight-binding model consisting of only In p orbitals. We predict this material to be a nodal line semimetal with Dirac crossings and topological surface states at the experimental Fermi level. This compound can be considered a 3D chemical analog of 2D square-net semimetals in the ZrSiS family, with primary p_x,y orbital contributions and cubic connectivity. LaIn₃ and related auricupride metals are established superconductors and may provide a valuable platform for exploring the interplay between the topological electronic structure and superconductivity.