Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery

Abstract

We identify all symmetry-enforced band crossings in nonmagnetic orthorhombic crystals with and without spin-orbit coupling and discuss their topological properties. We find that orthorhombic crystals can host a large number of different band degeneracies, including movable Weyl and Dirac points with hourglass dispersions, fourfold double Weyl points, Weyl and Dirac nodal lines, almost movable nodal lines, nodal chains, and topological nodal planes. Interestingly, spin-orbit coupled materials in space groups 18, 36, 44, 45, and 46 can have band pairs with only two Weyl points in the entire Brillouin zone. This results in simpler connectivity of the Fermi arcs and more pronounced topological responses than in materials with four or more Weyl points. In addition, we show that the symmetries of space groups 56, 61, and 62 enforce nontrivial weak Z2 topology in materials with strong spin-orbit coupling, leading to helical surface states. With these classification results in hand, we perform extensive database searches for orthorhombic materials crystallizing in the relevant space groups. We find that Sr2Bi3 and Ir2Si have bands crossing the Fermi energy with a symmetry-enforced nontrivial Z2 invariant, CuIrB possesses nodal chains near the Fermi energy, Pd7Se4 and Ag2Se exhibit fourfold double Weyl points, the latter one even in the absence of spin-orbit coupling, whereas the fourfold degeneracies in AuTlSb are made up from intersecting nodal lines. For each of these examples, we compute the ab initio band structures, discuss their topologies, and for some cases also calculate the surface states.