Topological Insulators

Topological insulators are characterized by insulating bulk and conducting surface, the latter is a necessity consequence of the nontrivial topology of the wavefunctions forming the valence band. This chapter gives a historical overview of the discovery of topological insulators and a concise description of the $Z_2$ topology which defines them. The concept of topological insulators have been extended to various other topologies, giving rise to the recognition of further topological states of matter such as topological crystalline insulators and higher-order topological insulators. Representative materials of topological insulators, their synthesis techniques, and the ways for the experimental confirmation of the topological nature are introduced. Among the interesting phenomena derived from topological insulators, topological superconductivity, Majorana zero modes, and quantum anomalous Hall effect are briefly discussed.