This month's Learnin' Corner, courtesy of Motherboard’s granddad Vice, is an explanation of topological matter in optical lattices by University of Pittsburgh associate professor of physics W. Vincent Liu, whose paper "Topological Matter in Optical Lattices" first interested us in the subject of topological matter in optical lattices.
This is a very special material whose bulk is an insulator (no currents can flow inside the system—for electron systems, it is electric current), but at the same time, its edge is metallic, along which currents can flow. For example, if we consider a two-dimensional electron-based topological insulator (which is a thin sheet), electronic currents cannot flow anywhere inside this sheet. Nevertheless, the edge of this sheet is like a wire, and currents can flow along the edge. In many cases, the edge current can only flow in one direction, known as chiral current, much like cars flowing on a one-way road or on one lane of the interstate highway.
Another interesting, and quite unexpected, property of topological insulators lies in the fact that the conductivity of the whole system is very sensitive to the shape (topology). For an ordinary insulator/metal, it is always an insulator/metal no matter what shape we made it into. However, for a topological insulator, if we make the sheet into a sphere, because the sphere has no edges, the system will turn into a true insulator, where currents cannot flow anywhere. But if we make the sheet into a disk, which has an edge, the system can conduct electronic currents due to the metallic edge. Read more here.
By W. Vincent Liu as told to Harry Cheadle