Robust spin-polarized midgap states at step edges of topological crystalline insulators.

Topological crystalline insulators are materials in which the crystalline symmetry leads to topologically protected surface states with a chiral spin texture, rendering them potential candidates for spintronics applications. In this talk, I report on the discovery of one-dimensional midgap states at odd-atomic surface step edges of the three- dimensional topological crystalline insulator (Pb,Sn)Se. A minimal toy model and realistic tight-binding calculations identify them as spin-polarized flat bands connecting two Dirac points. The midgap states inherit stability through the two-dimensional Dirac metal from the three-dimensional bulk insulator. This makes (Pb,Sn)Se the first example for a crystal symmetry-protected hierarchy of one- and two dimensional topological modes, which we experimentally prove to result in a striking robustness to defects, strong magnetic fields, and elevated temperature.