Fulde-Ferrell state induced purely by the orbital effect in a superconducting nanowire

We demonstrate that the Fulde-Ferrell (FF) phase can be induced uniquely by the orbital effect in a cylindrical metallic nanowire. In the external magnetic field the two-fold degeneracy with respect to the orbital quantum number $m$ is lifted what leads to a Fermi wave vector mismatch between the subbands with opposite orbital momenta in the paired state. This mismatch can be compensated by the nonzero total momentum of the Cooper pairs created by electrons from split subbands what results in the formation of the FF phase. With increasing magnetic field a series of FF stability regions appear in between which the standard BCS superconducting phase is stable.