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

TL;DR

This paper classifies higher-order topological semimetals and nodal superconductors with order-two crystalline symmetries, revealing diverse hinge states and their relation to bulk topology.

Contribution

It systematically classifies all higher-order topological phases with order-two crystalline symmetries across tenfold classes, identifying new hinge state phenomena.

Findings

Identification of four types of higher-order topological phases

Relation between hinge states and bulk topology

Comprehensive classification across symmetry classes

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.