Preface to the special topic on topological insulators

Abstract

The most important aspect of condensed matter physics in the last century has been the classification of quantum states in terms of spontaneous symmetry breaking. In 1980, the quantum Hall state—which is independent of material details and topologically different from the previously known states of matter— was discovered in the two-dimensional electron gas under an external magnetic field. Two years later, the fractional quantum Hall state was discovered in a similar two-dimensional system. The quantum Hall states belong to a topological class that has no spontaneously broken symmetry. The physical behaviors of the system depend only on its topology and not on its particular geometry. Very recently, a completely new class of states, called topological insulators, has emerged. Topological insulators have a bulk energy gap and gapless edge/surface states that are protected by the time-reversal symmetry and immune to impurities and geometric perturbations. To form such new states, the coupling between the spin and the orbital motion must be strong. Therefore, topological insulator states usually occur in a compound material that is composed of heavy elements. Because of the many exotic phenomena—including the quantum spin Hall effect, the quantum anomalous Hall effect, a magnetic monopole and Majorana fermions—that can exist in topological insulators, this new class of topological states has attracted increasing attention over the last seven years and has largely revolutionized modern condensed matter physics. We selected this particularly interesting area of topological insulators for our first issue ofNational Science Review.The issue contains a general review on topological phases in condensed matter physics by Shunqing Shen, and a review on the newly discovered quantized anomalous Hall effect by Ke He. The interesting story behind this discovery is presented in an interview to Xucun Ma. In a perspective article by Canhua Liu and Jinfeng Jia, they discuss methods to createMajorana fermions with topological insulators. Peizhe Tang and Wenhui Duan report their recent work on the quantum anomalous Hall effect in materials with in-plane magnetization, while Feng Liu and JianWu discuss new organic topological materials in two research highlight articles, respectively. In a perspective article, Kai Chang discusses topological insulating phases in commonly used semiconductors. As the guest editor of this special topic in the inaugural issue, I would like to take this opportunity to thank these authors for their generous contributions. The research of topological insulators is just at its very beginning. I believe further progress will be made in the near future and hope that the special topic can provide some useful information and promote research in this rapidly developing field. Last but not least, I would like to thank the editorial staff ofNational Natural Science for their sustained support during the preparation of this special issue.