TeI*

The established diversity of electronic topology classes lends the opportunity to pair them into dual topological complexes. We show that the layered compound Bi₂TeI realizes a dual topological insulator. It exhibits band inversions at two time reversal symmetry points of the bulk band which classify it as a weak topological insulator. Additional mirror symmetry of the crystal structure concurrently classifies it as a topological crystalline insulator. Bi₂TeI is therefore predicted to host a pair of Dirac cones protected by time reversal symmetry on its ’side’ surfaces and three pairs of Dirac cones protected by mirror symmetry on its top and bottom surfaces. We spectroscopically map the top cleaved surface of Bi₂TeI, and crystallographic step edges therein. We show the existence of both two dimensional surface states which are susceptible to mirror symmetry breaking, as well as one dimensional channels that reside along the step edges. Their mutual coexistence on the step edge where both facets join is facilitated by momentum and energy segregation.