1D FFLO state in absence of time reversal symmetry breaking

We propose a route to a one-dimensional Fulde-Ferrell-Larkin-Ovchinnikov state in the absence of broken time-reversal symmetry. At present such a state may be encouraged in a clean (no disorder) AlAs quantum wire fabricated using the cleaved edge overgrowth technique. The fabrication technique captures two degenerate nonoverlapping bands separated in momentum-space by half an umklapp vector which leads to four Fermi points. Using field theoretic methods such as abelian bosonization and the renormalization group scheme we treat the important low energy long wavelength fermionic interaction terms for this one dimensional system. Due to the specific bandstructure arrangement of the quantum wire there is a new class of unique umklapp assisted interactions. These umklapp interactions are present at all electronic densities and are not related to the commensurability of the electron gas with the underlying lattice. We show that in the presence of the umklapp interactions and without any external perturbations such as a magnetic or electric field a singlet superconducting ground state is preferred with non-zero center-of-mass momentum for the Cooper pairs. The finite pairing momentum of the Cooper pairs is an indication of a Fulde-Ferrell-Larkin-Ovchinnikov state which is known to lead to inhomogeneous superconductivity.