摘要：
Recently, a new class of topological states has been proposed and experimentally realized. These topological insulators have an insulating gap in the bulk, but have topologically protected edge or surface states due to the time reversal symmetry. In two dimensions the edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. I shall review the theoretical prediction of the QSH state in HgTe/CdTe semiconductor quantum wells, and its recent experimental observation. The edge states of the QSH state supports fractionally charged excitations. The QSH effect can be generalized to three dimensions as the topological magneto-electric effect (TME) of the topological insulators. Bi2Te3, Bi2Se3 and Sb2Te3 are theoretically predicted to be topological insulators with a single Dirac cone on the surface. I shall present a realistic experimental proposals to observe the magnetic monopoles on the surface of topological insulators.