Various electron dispersions that can lead to a topologically nontrivial superconducting state with Majorana fermion excitations. Red bands represent occupied single-electron states and the arrows indicate the orientation of electron spins. (a) Parabolic dispersion characteristic of a 2D electron gas with negligible spin-orbit coupling. For each momentum k there are two degenerate spin projections. In this case, electrons must be paired with an unconventional spin-triplet px+ipy order parameter to produce a topological superconductor . (b) Helical liquid on the surface of a topological insulator characterized by Dirac energy dispersion. There is one spin state at each momentum k with orientation perpendicular to k. An ordinary s-wave pairing leads to topological superconductivity . (c) 2D electron gas with strong spin-orbit coupling in the presence of ferromagnetic insulator or in-plane magnetic field discussed in Refs. [3, 8]. The upward canting of spins signifies broken time-reversal invariance. In this case, an s-wave pair potential induced by the proximity effect generates a topological superconductor characterized by a mixture of the spin-singlet s-wave and spin-triplet p-wave order parameters.