Topological insulators and superconductors

Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory…