  A novel route to a one-dimensional Fulde-Ferrell-Larkin-Ovchinnikov (1D-FFLO)
state in the absence of broken time-reversal symmetry is proposed in this
paper. At present such a state may be encouraged in a clean AlAs quantum wire.
Using the AlAs quantum wire as an example it is shown using bosonization and
the renormalization group approach that the 1D-FFLO state can arise due to a
combination of Coulomb interactions and the unique bandstructure arrangement of
the AlAs quantum wire. The present theoretical proposal is very general and is
applicable to other systems with similar fermionic interaction terms.
