Topological insulators are band insulators with topologically nontrivial quantum ground states. The study about these novel states of matter has improved our understanding of the quantum world. In addition, concepts and ideas developed from these studies have also been benefiting research activities in other subareas of physics and materials science. For example, on the experimental side, these topological states are characterized by a gapped insulating bulk and topologically-protected metallic surfaces with spin-momentum locking. These novel surface states offer a new platform for the study of 2D charge/spin transport and can be used to create new electronic devices, e.g., topological spintronics. One other interesting extension about topological insulators lies in strong-correlation effects. In strongly-correlated materials, topologically-nontrivial insulating states can also be stabilized, where interactions play an essential role and strong correlation effects arise naturally. Furthermore, studies on topological insulators have also motivated physicists to explore other topological states beyond insulators, e.g., topological superconductors and topological semi-metals, which will also be discussed in this tutorial.
This tutorial will provide an introduction about basic ideas and tools for the study of topological states of matter, including theory, experiments, and materials synthesis. The lectures will discuss fundamental questions about topological insulators, as well as its interplay with other subfields of condensed matter physics, including strongly-correlated topological insulators, topological spintronics, topological semi-metals, etc.