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We study spin-half fermions in a one-dimensional extended Hubbard chain atlow filling. We identify three triplet and one singlet pairing channels in thesystem, which are independently tunable as a function of nearest-neighborcharge and spin interactions. In a large-size system with translationalinvariance, we derive gap equations for the corresponding pairing gaps andobtain a Bogoliubov-de Gennes Hamiltonian with its non-trivial topologydetermined by the interplay of these gaps. In an open-end system with a fixednumber of particles, we compute the exact many-body ground state and identifythe dominant pairing revealed by the pair density matrix. Both cases showcompetition between the four pairing states, resulting in broad regions foreach of them and relatively narrow regions for mixed-pairing states in theparameter space. Our results enable the possibility of tuning a nanowirebetween singlet and triplet pairing states without breaking time-reversal orSU(2) symmetry, accompanied by a change in the system's topology.

Tuning between singlet, triplet, and mixed pairing states in an extended Hubbard chain