Topological Insulators

The recent discovery of a new class of materials, the so-called topological insulators [1–5]. has generated a great interest in the fields of condensed matter physics and materials science [1]. In principle, according to their band structure, compounds can be divided into metals and insulators. Recently a new class of the so-called topological states has emerged, the Quantum Spin Hall (QSH) state in two and three dimensions. The respective materials are called "topological insulators". The 3D topological insulators have a full insulating gap in the bulk, but a topological protected gapless surface or edge states on the boundary [6–8]. Additionally the 2D topological insulators (e.g. HgTe [9, 10], are metallic in the bulk, but can be designed as topological insulators in quantum well structures with a trivial semiconductors such as CdTe. A topological insulator can easily be identified by a few simple rules: the presents of a large spin orbit coupling, an odd number of band inversions between the conduction and the valence band by increasing the average nuclear charge, and a sign change of the symmetry of the molecular orbitals [11]. Similiar features are favorable for thermoelectric properties, thus topological insulators may be good thermoelectric materials and vice versa. Here we present a short introduction to topological insulators and give examples of compound classes where both topological insulators and good thermoelectric properties can be found.