Majorana fermions in a two-band two-dimensional Fermi system

Majorana fermions represent potential candidates for realizing fault -tolerant topological quantum computation. We obtain the exact mapping between a two -band hybridized model and a model with a topological superconducting state supporting Majorana fermions. The antisymmetric hybridization employed resembles that of spin-orbit coupling. We consider the situation where the model Hamiltonian comprises only inter -band s -wave pairing, i.e. the one in which the superconducting pairing is formed by one fermion from one of the bands and another fermion of opposite spin and momentum from the other band. From this we obtain an effective Hamiltonian of the px + ipy superconductor and calculate the topological invariant that distinguishes the weak and strong pairing phases. We also obtain the gap parameter and chemical potential of the Fermi system under spin-orbit coupling beyond the mean -field approximation. We show that the spin-orbit coupling substantially enhances the density of states at the Fermi surface.