A thin wire made of a special material, a topological insulator, behaves like a city street: the interior is empty, and all traffic runs along the edges. Electrons in such a wire move only along the surface, like pedestrians on a sidewalk, never stepping onto the roadway. But if the street is messy (potholes, puddles, construction barriers) pedestrians start tripping, and electrons start scattering and getting stuck.

Scientists added a magnetic field threading through the wire, like a stream of cars regulated by a traffic light. It turned out that at a certain strength of this flux, half a quantum of magnetic flux, the disorder stops interfering. Electrons that used to get stuck at every step suddenly run freely along the wire's edge. It's as if all the potholes on the sidewalk vanished at once, and pedestrians could walk with a steady stride.

The researchers measured how far an electron can travel without getting stuck: this distance is called the localization length. They found that near this special value of magnetic flux, the localization length increases sharply, as if the sidewalk became perfectly smooth for many kilometers. Surprisingly, this property does not depend on how much disorder is in the wire or what the electron energy is: you always get the same number characterizing the transition.

This number is the exponent with which the localization length grows as you approach the special flux. It equals two. For comparison, in another well-known quantum phenomenon, the integer quantum Hall effect, this exponent is different. This means the transition in the topological nanowire is organized differently, and this is important for understanding how to control electrons at the nanoscale.

At another value of magnetic flux, a whole quantum, the wire's behavior changes: at low electron energy, conductivity drops, while at high energy, it increases. It's as if on the same street, in one case additional potholes appear, and in another, new asphalt is laid. Understanding such transitions will help create more reliable and faster electronic devices where current flows without losses.