Tuning between s-wave and p-wave superconductors as well as emerging Majorana fermions in extended Hubbard lattices

We study spin-half fermions in one dimensional extended Hubbard lattices in which the superconducting pairing orders are induced by the tuning of nearest-neighbor charge and spin interactions. We derive gap equations for three p-wave (triplet) as well as one s-wave (singlet) pairing orders and obtain a phase diagram characterizing these orders as a function of interaction couplings. We find that the system can evolve between s-wave and p-wave pairing states, accompanied with the emergence of Majorana fermions in the p-wave regime, identified as a time-reversal invariant Kitaev Majorana chain. Finally we discuss the effects on the topological non-trivial states when time-reversal or SU(2) symmetry breaks.