Nematic superconductivity in a one-dimensional system of massless fermions

The superconducting properties of the one-dimensional model of "relativistic " fermions with attraction generated by antiferromagnetic (Heisenberg) pair superexchange spin interaction are studied. Namely, we demonstrate that such a pairing in this system takes place in the nematic channel, with extended s-wave symmetry, where the attraction between fermions mostly takes place when the fermions occupy the nearest sites. It is demonstrated, that the zero-temperature properties of such a system are rather different from the "standard " case of superconductivity with local attraction. For instance, the order parameter has an unusual helical momentum dependence, & SIM; e - i k a, where a is the lattice parameter and the dependence of the gap on doping has a bell shape, qualitatively similar to cuprate high-T-c superconductors. Finally, the smooth transition from the overlapping pair to the local pair regime (or BCS-BEC crossover) in the nematic phase takes place at much lower values of doping as compared to the local pairing case, i.e., the "relativistic 1D " nematic superconductor is much less "friendly " to the local pairs. We also discuss the possible relation of the properties of this model to the superconducting properties of twisted graphene. Published under an exclusive license by AIP Publishing.