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

We show that the Fulde-Ferrell (FF) phase may appear as a sole result of the orbital effect in a cylindrical metallic nanowire. Namely, in the external magnetic field the twofold degeneracy with respect to the orbital magnetic quantum number m is lifted, which 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 the split subbands which results in the formation of the FF phase. In this manner, a transformation of the orbital motion into a linear supercurrent parallel to the applied field is taking place. With the increasing magnetic field a series of FF stability regions appear, in between which the standard BCS superconducting phase is stable. For the sake of completeness, we show, that the inclusion of the Zeeman term in the model does not change the picture qualitatively, particularly if larger m states contribute essentially to the Fermi-surface splitting. A brief but important note concerning the possibility of steering the supercurrent by an applied magnetic field parallel to it, is also provided.