Topological Insulators

Topological Insulators, volume six in the Contemporary Concepts of Condensed Matter Series, describes the recent revolution in condensed matter physics that occurred in our understanding of crystalline solids. The book chronicles the work done worldwide that led to these discoveries and provides the reader with a comprehensive overview of the field.

Starting in 2004, theorists began to explore the effect of topology on the physics of band insulators, a field previously considered well understood. However, the inclusion of topology brings key new elements into this old field. Whereas it was thought that all band insulators are essentially equivalent, the new theory predicts two distinct classes of band insulators in two spatial dimensions and 16 classes in three dimensions. These "topological" insulators exhibit a host of unusual physical properties, including topologically protected gapless surface states and exotic electromagnetic response, previously thought impossible in such systems.

Within a short time, this new state of quantum matter, topological insulators, has been discovered experimentally both in 2D thin film structures and in 3D crystals and alloys. It appears that topological insulators are quite common in nature, and there are dozens of confirmed substances that exhibit this behavior. Theoretical and experimental studies of these materials are ongoing with the goal of attaining the fundamental understanding and exploiting them in future practical applications.

1. Topological band theory and the Z2 invariant, Charles Kane
2. Topological insulators in 3D, Joel Moore
3. Models and materials for topological insulators, Chaoxing Liu & Shou-Cheng Zhang
4. Field-theoretic foundations of topological insulators, Xiao-Liang Qi
5. Quantum spin Hall state in HgTe, C. Brüne, H. Buhmann & Laurens Molenkamp
6. Topological surface states: A new type of 2D electron systems, Su-Yang Xu, David Hsieh, L. Andrew Wray, Yuqi Xia & Zahid Hasan
7. Topological surface states imaging by STM, Haim Beindenkopf, Pedram Roushan & Ali Yazdani
8. Transport properties, Jeroen B. Oostinga, & Alberto F. Morpurgo
9. New materials, Ke He, Xucun Ma, Xi Chen & Qi-Kun Xue
10. Related states of quantum matter, Ari Turner & Ashvin Vishwanath
11. Theoretical design of materials and functions of topological insulators and superconductors, Naoto Nagaosa