  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.
