Spin-momentum locking in the topological insulator allows symmetry-protected surface states to host Majorana particles if superconductivity is induced on the surface of 3D topological insulators via proximity effects. (Note that Majorana zero-mode can also appear without topological insulators.) The non-trivialness of topological insulators is encoded in the existence of a gas of helical Dirac fermions. Dirac particles which behave like massless relativistic fermions have been observed in 3D topological insulators. Note that the gapless surface states of topological insulators differ from those in the quantum Hall effect : the gapless surface states of topological insulators are symmetry-protected (i.e., not topological), while the gapless surface states in quantum Hall effect are topological (i.e., robust against any local perturbations that can break all the symmetries). The Z 2 topological invariants cannot be measured using traditional transport methods, such as spin Hall conductance, and the transport is not quantized by the Z 2 invariants. An experimental method to measure Z 2 topological invariants was demonstrated which provide a measure of the Z 2 topological order. (Note that the term Z 2 topological order has also been used to describe the topological order with emergent Z 2 gauge theory discovered in 1991.) More generally (in what is known as the ten-fold way) for each spatial dimensionality, each of the ten Altland—Zirnbauer symmetry classes of random Hamiltonians labelled by the type of discrete symmetry (time-reversal symmetry, particle-hole symmetry, and chiral symmetry) has a corresponding group of topological invariants (either Z , Z 2 or trivial) as described by the periodic table of topological invariants.