A chain of red phosphorus atoms is like a train where the cars are atoms and the couplers are chemical bonds. Sometimes the couplers are stronger, sometimes weaker, and that affects how electrons run through the train.
Physicists took this chain and calculated under what conditions electrons can move and when they get stuck. It turned out that at a certain ratio of coupler strengths, a rearrangement occurs: electrons that were previously stuck suddenly gain the ability to run, and vice versa. It's as if the couplers between train cars were swapped, and passengers in some cars could suddenly move to others.
This rearrangement leaves a trace at the chain's edges: special states appear there, visible in the spectrum. The scientists didn't just check this on paper but also experimentally: they built a mimic of the phosphorus chain from an aluminum plate with holes and saw the same edge states. This means that phosphorus topology can be studied not only through calculations but also on a macroscopic model.
Red phosphorus isn't a single substance but a whole family of different structures. The one considered in this work consists of one-dimensional chains of phosphorus atoms.