Symmetry-Enforced Weak Topology in Dirac Semimetals

Conventional topological insulators result from band inversions. As such their existence is dependent on the details of the system. In the present work we discuss certain space groups that lead to a nontrivial arrangement of parity eigenvalues in a 2D subset of the 3D Brillouin zone. Consequently, all materials with the corresponding crystalline symmetries exhibit a nontrivial weak topological invariant. While, as a whole, these systems are filling-enforced semimetals, the nontrivial gapped subsystems imply the existence of surface states. We discuss several examples of such enforced topology among orthorhombic and tetragonal space groups using general symmetry arguments and tight-binding models. Supported by DFT calculations we propose two example materials, Sr₂Bi₃ and Ir₂Si that realize the enforced weak topology in the vicinity of the Fermi energy.