Introduction to the Topological Insulators and State of the Art

In this chapter a brief introduction to the world of topological condensed matter is presented. Firstly, the quantum Hall state in a two dimensional electron gas (2DEG) is introduced. After, the prediction and the subsequent experimental discovery of a topological insulating state of spin-orbit origin is presented. In particular, the so-called strong three dimensional topological insulators (3D TIs) are the object of this thesis. The second part of this chapter focuses on specific 3D TI materials. After their chemical description, their transport and surface properties are reported together with previous optical measurement results.