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The orbital effect on the Fulde-Ferrell (FF) phase is investigated insuperconducting core/shell nanowires subjected to the axial magnetic field. Theconfinement in the radial direction results in the quantization of the electronmotion with energies determined by the radial $j$ and orbital $m$ quantumnumbers. In the external magnetic field the twofold degeneracy with respect tothe orbital magnetic quantum number $m$ is lifted which leads to the Fermi wavevector mismatch between the paired electrons $(k, j,m,\uparrow) \leftrightarrow(-k, j,-m,\downarrow)$. This mismatch is transfered to the nonzero totalmomentum of the Cooper pairs which results in the formation of FF phaseoccurring sequentially with increasing magnetic field. By changing the nanowireradius $R$ and the superconducting shell thickness $d$, we discuss the role ofthe orbital effect in the FF phase formation in both the nanowire-like ($R/d\ll 1$) and nanofilm-like ($R/d \gg 1$) regime. We have found that theirregular pattern of the FF phase, which appears for the case of thenanowire-like regime, evolves towards the regular distribution, in which the FFphase stability regions appear periodically between the BCS state, for thenanofilm-like geometry. The crossover between these two different phasediagrams is explained as resulting from the orbital effect and the multigapcharacter of superconductivity in core/shell nanowires.

Fulde-Ferrell state in superconducting core/shell nanowires: role of the orbital effect