Physicists classify and understand systems in terms of many properties; color, mass, and length are familiar examples. The theme of this Quick Study is a more subtle property—a system’s topology, or how its parts connect. As an example, a circular linked necklace can be deformed into an oval or a rectangle without changing the topology, since the links remain connected in the same way. But the necklace can only be made into the topologically distinct straight line if it is cut or its clasp is opened. In the 1980s physicists realized that some physical properties are entirely dictated by a system’s topology.
The exemplar of a topological phenomenon is the quantum Hall effect (see Physics Today, December 1985, page 17). Consider a charged particle confined to a two-dimensional plane. When a magnetic field is applied perpendicular to the plane, the charged particle will undergo circular cyclotron motion.
The...
