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

Abstract

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.

5 + 13 pages, 1 + 2 figures, v2: published version, added appendix on topological invariants

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Cited by in corpus (10)

• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Thermodynamic transitions and topology of spin-triplet superconductivity: Application to UTe${}_2$
• Crystalline-electromagnetic responses of higher order topological semimetals
• Topological Insulators with Hybrid-order Boundary States
• Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Perfectly localized Majorana corner modes in fermionic lattices
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn