Emerging trends in Topological Insulator and Topological Superconductor

Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of spin-orbit coupling and time reversal symmetry. Also these states are insensitive to scattering by non-magnetic impurities. A two-dimensional (2D) topological insulator has one dimensional (1D) edge states in which the spin-momentum locking of the electrons gives rise to quantum spin Hall effect. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. These topological insulator materials have been theoretically predicted and experimentally observed in a variety of 2D and 3D systems, including $\rm HgTe$ quantum wells, $\rm BiSb$ alloys, and $\rm Bi_{2}Te_{3}$, $\rm Bi_{2}Se_{3}$ crystals. Moreover, proximity induced superconductivity in these systems can lead to a state that supports zero energy Majorana fermion and the phase is known as topological superconductors. In this article, the basic idea of topological insulators and topological superconductors are presented along with their experimental development.