Much of condensed matter physics is concerned with understanding how different kinds of order emerge from interactions between a large number of simple constituents. In ordered phases such as crystals, magnets, and superfluids, the order is understood through "symmetry breaking": in a crystal, for example, the continuous symmetry of space under rotations and translations is not reflected in the ground state, which instead has a periodic arrangement of ions. A major discovery of the 1980s was that electrons confined to two dimensions and in a strong magnetic field exhibit a completely different, "topological" type of order that underlies the quantum Hall effect. A discovery in the last few years is that topological order also occurs in some three-dimensional materials, dubbed "topological insulators", in zero magnetic field. Spin-orbit coupling, an intrinsic property of all solids, drives the formation of the topological state.
This talk will explain what topological order means, how topological insulators were discovered, and how they realize the "axion electrodynamics" studied by particle physicists in the 1980s. A possible application of these new materials is discussed in closing.