Physical Society Colloquium

New Topologically Ordered Phases of Condensed Matter

Joel E. Moore

University of California, Berkeley

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 symmetries of space under rotations and translations are not reflected in the ground state. 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.