[@samokhin_magnetic_2004; @barzykin_inhomogeneous_2002]. This latter feature was first observed in the bulk non-centrosymmetric heavy fermion superconductor CePt$_3$Si [@bauer_heavy_2004] and shortly after in CeRhSi$_3$ [@kimura_pressure-induced_2005] and CeIrSi$_3$ [@sugitani_pressure-induced_2006]. Moreover, it has been predicted that the interplay between an in-plane magnetic field and SOC in a surface superconductor would lead to an inhomogeneous superconducting phase [@barzykin_inhomogeneous_2002; @dimitrova_theory_2007; @agterberg_magnetic-field-induced_2007], similar to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase [@fulde_superconductivity_1964; @larkin_nonuniform_1964]. Low dimensional systems were recently fabricated using strong spin-orbit coupled semiconducting epitaxial InAsSb nanowires coated by an extremely thin layer of superconducting aluminium [@krogstrup_epitaxy_2015; @Sestoft:2018] or in 2D platforms suitable for manipulating Majorana end states [@shabani:2016]. Besides the Majorana physics, such low-dimensional systems should also display a superconducting modulated phase. Moreover, such a modulated phase is characterized by the rotation of the superconducting phase along the wire, which produces a ground state with a finite phase difference $\varphi_0$ for a finite length wire used as a weak link [@krive_influence_2005; @buzdin_direct_2008; @reynoso_anomalous_2008; @zazunov:2009]. Recently such $\varphi_0$-Josephson junction has been realized experimentally in nanowire quantum dots [@szombati_josephson_2016].

The inhomogeneous FFLO state originates from the interaction of the superconducting condensate with a Zeeman field (see [@matsuda_fulde-ferrell-larkin-ovchinnikov_2007] as a review). The latter causes a spin-splitting, which in turn leads to Cooper 