Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry

Using a systematic relation between topological gapless phases in three dimensions and topological gapped phases in two dimensions, we identify four types of higher-order topological semimetals or nodal superconductors (HOTS), hosting (i) flat zero-energy ???Fermi arcs??? at crystal hinges, (ii) flat zero-energy hinge arcs coexisting with surface Dirac cones, (iii) chiral or helical hinge modes, or (iv) flat zero-energy hinge arcs connecting nodes only at finite momentum. Bulk-boundary correspondence relates the hinge states to the bulk topology protecting the nodal point or loop. We classify all HOTS for all tenfold-way classes with an order-two crystalline (anti)symmetry, such as mirror, twofold rotation, or inversion.

Automated summary

Using the relationship between topological gapless phases in three dimensions and topological gapped phases in two dimensions, this study identifies four types of higher-order topological semimetals or nodal superconductors (HOTS), each exhibiting different characteristics at crystal hinges, with their properties corresponding to the bulk topology.