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Observation of robust one-dimensional edge channels in a three-dimensional quantum spin Hall insulator

Topologically protected edge channels show prospects for quantum devices. They have been found experimentally in two-dimensional (2D) quantum spin Hall insulators (QSHIs), weak topological insulators and higher-order topological insulators (HOTIs), but the number of materials realizing these topologies is still quite limited. Here, we provide evidence for topological edge states within a novel topology named three-dimensional (3D) QSHIs. Its topology originates solely from a nonzero $S_z$ spin Chern number for each $k_z$ plane of the crystal and is realized in bulk $α$-Bi$_4$I$_4$ with trivial symmetry indicators, as we show by density functional theory calculations. We experimentally observe the related edge states at each type of monolayer and bilayer step of this material by scanning tunneling microscopy. Consistently, the edge states are neither interrupted, nor backscattered by defects at the step edges corroborating their helical character as expected from the nontrivial topology. Furthermore, two individual edge channels are directly observed at bilayer steps without visible interaction gap opening, demonstrating the robustness of these edge modes against vertical stacking. Our results establish $α$-Bi$_4$I$_4$ as the first material realization of a 3D QSHI whose definition goes beyond the scope of topological symmetry indicators, and provide a pathway for realizing nearly-quantized spin Hall conductivity per unit cell in a bulk crystal.