Topological phase transitions driven by next-nearest-neighbor hopping in noncentrosymmetric cold Fermi gases

We investigate the topological phase marked by the Thouless-Kohmoto-Nightingale-Nijs (TKNN) number and the phase transitions driven by the next nearest neighbor (NNN) hopping in noncentrosymmetric cold Fermi gases, both spin-singlet pairing and spin-triplet pairing are considered. There exists a critical t'_c for the NNN hopping, at which the quantum phase transition occurs, and the system changes from an Abelian (non-Abelian) phase to a non-Abelian (Abelian) one. By numerically diagonalizing the Hamiltonian in the real space, the energy spectra with edge states for different topological phases and the Majorana zero modes are discussed. Although the spin-triplet pairing does not contribute to the gap closing and the phase diagram, it induces gapless states in the presence of a magnetic field, and the TKNN number in this region is still zero.