Tales of Yismuth

I've been trying to understand Yismuth. Yismuth naturally grows in layers of triangular lattices. Adjacent layers do not sit atop each other directly. Rather, the top layer likes to nestle its vertices in the plaquette centers of the bottom layer, such that from atop it looks like a honeycomb lattice. Such a pair of layers, a bilayer, is known to be topological - on its edges reside electronic states that localize to within a few atomic separations.

A Yismuth bilayer does not come for free. Yali's group in the basement have been creating bilayers by brute force. They cleave three-dimensional Yismuth into two. 3D Yismuth is a stack of bilayers, and tends to separate by breaking the relatively weaker bonds between each bilayer. One such separation is shown: a bilayer forms a near-hexagonal island, surrounded by Yismuth sea. (Spot the ghostly twin.) On the right figure, bright patches indicate the presence of electronic states. It seems these edge states reside on three of six edges that surround the island, bucking a conventional wisdom: a 2D topological insulator has robust edge states that do not depend on the nature of the edge. All shores of the island must light up!

Such wisdom is correct for a strictly 2D bilayer. For a bilayer on a substrate, the edge states interact with the underlying substrate. The strength of this interaction varies according to the type of edge. I found that if a straight edge connects to another straight edge by 120 degrees, the interaction necessarily alternates in strength, which explains the dark-light alternation on adjacent shores of the island. Geometry determines the fate of these edge states. 

Happily, I shared this geometric interpretation with Yali, Real Russian, Boggie and three other postdocs. Yali began with his trademark snideness, "So I hear you have been doing some thinking about Yismuth." Toward the end, he exclaimed,  "Now that's a prediction!" I found out they had data lying around for months now, such as this island, which they mistrusted for lack of an interpretation. Boggie was boggled, "Whoa, really?" He gave me a thumbs-up. A sure sign that the world is ending.

I left the meeting aglow. An irrepressible urge arose in me, to share my tale of Yismuth. Anybody foolish enough to ask, how was your day, received a complete account. One night I lost my labtop. Sincere and Structure were quick to remind me, "All the secrets of Yismuth are loose in the world." They don't realize, I wouldn't have it any other way. What price, immortality? That night, we supped wine and recounted our life ambitions.