Figure 1: 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 [6]. (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 [7]. (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.