Hinge states in SnTe

Three-dimensional topological insulators are materials with an insulating bulk, but conducting surface states topologically protected by time-reversal symmetry. 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, where we distinguish 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 topology is Z2 classified. (2) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs and the topology is Z classified. Furthermore we show that uniaxially strained SnTe is a helical higher-order topological insulator with one Kramers pair of gapless modes on each hinge.