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. A major
discovery of the 1980s was that electrons confined to two dimensions and
in a strong magnetic field exhibit a completely different, "topological" order
in the quantum Hall regime. Topological order was recently discovered 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. The first part of the talk will explain how
topological insulators were predicted and discovered by building on the
quantum Hall effect. The second part will cover more recent work on
connections between topological insulators, magnetoelectric effects ("axion
electrodynamics"), and strong correlation effects.
