# Synopsis: A topological metal in one dimension

The finding of one-dimensional, topologically protected conducting states on the surface of bismuth suggests the possibility of a quantum spin Hall effect in one dimension.

Conducting one-dimensional channels were known to exist at the edges of quantum Hall systems. Recently, similar metallic states were also discovered along the edges and surfaces of certain band insulators with large spin-orbit coupling, such as $\text{HgTe}$ quantum wells and $\text{Bi-Sb}$ alloy, respectively. These unusual metallic states constitute a pair with opposite spin and electron momentum and are “topologically protected” because deformations or addition of impurities to the surface can modify the conduction and valence-band states but cannot open a gap between them.

In Physical Review Letters, Justin Wells and colleagues from the University of Aarhus in Denmark, along with a multinational list of collaborators from Switzerland, Russia, Germany, and Spain report the finding of a one-dimensional topological spin-split surface metallic state on the $\left(114\right)$ surface of bismuth using scanning tunneling microscopy and photoemission spectroscopy. A reconstruction on this surface of bismuth produces straight atomic rows in the $x$ direction with a wide separation in the $y$ direction, giving rise to the one-dimensional character. Since bismuth is a semimetal and not an insulator, this surface state lies partly inside the bulk continuum of states. In contrast to the case of higher dimensions, spins in the one-dimensional topological metallic state are aligned with the momentum of the electrons rather than being perpendicular to it. The authors also predict that the same surface state is likely to be present in insulating ${\text{Bi}}_{0.9}{\text{Sb}}_{0.1}$ to give rise to a one-dimensional quantum spin Hall phase. – Sarma Kancharla

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