The quantum spin Hall effect and topological insulators

In the quantum world, atoms and their electrons can form many different states of matter, such as crystalline solids, magnets, and superconductors. Those different states can be classified by the symmetries they spontaneously break - translational, rotational, and gauge symmetries, respectively, for the examples above. Before 1980 all states of matter in condensed-matter systems could be classified by the principle of broken symmetry. The quantum Hall (QH) state, discovered in 1980, provided the first example of a quantum state that has no spontaneously broken symmetry. Its behavior depends only on its topology and not on its specific geometry; it was topologically distinct from all previously known states of matter. © 2010 American Institute of Physics.