Higher-Order Topological Insulators

Understand

Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries.

• Here, we extend the notion of three-dimensional topological insulators to systems that host no gapless surface states, but exhibit topologically protected gapless hinge states.
• Their topological character is protected by spatio-temporal symmetries, of which we present two cases: (1) Chiral higher-order topological insulators protected by the combination of time-reversal and a four-fold rotation symmetry.
• Their hinge states are chiral modes and the bulk topology is $\mathbb{Z}_2$-classified.