A few days ago, the Nobel Prize in Physics was awarded to Haldane, Kosterlitz, and Thouless, ”for theoretical discoveries of topological phase transitions and topological phases of matter”. Hey, I recognize two of those names! In my field of research, superconductivity, there’s something known as the Berezinskiĭ-Kosterlitz-Thouless transition. (Berezinskiĭ didn’t win the Nobel because he died in 1980.)
As always, the Nobel provides an article explaining the background for popular audiences. I’m just going to talk about it briefly to give you the gist.
Berezinskiĭ, Kosterlitz, and Thouless (BKT) explained the superconducting transition in flat, 2-dimensional materials. Below a certain temperature, the material becomes a superconductor, conducting electricity with precisely zero resistance. Above that temperature, it behaves as a normal material. What changes?
Superconductors have topological defects called vortices (singular form is “vortex”), which I depict below:

Here, each blue circle is an atomic site, and the arrow represents the “phase” of the superconductor. The two squares above show the two kinds of vortices, the “+” vortex and “-” vortex. These vortices behave as electrical charges, with like repelling like, and opposite charges attracting. [Read more…]


