pairs with a finite total momentum. For certain values of the Zeeman field and temperature, the ground state has an oscillating superconducting order parameter: $\Delta(\vec{r}) \propto e^{\text{i}\vec{q}\cdot\vec{r}}$, where $\vec{q}$ is the total momentum of the Cooper pairs. As shown in Fig. \[FFLO-diag\], in the absence of spin-orbit coupling, the FFLO state appears at low temperatures and high magnetic field. The transition between the normal and the FFLO states is of second order [@buzdin_nonuniform_1987; @buzdin_generalized_1997] in the ballistic limit.

In a superconducting system, the interplay between Zeeman field $\vec{h}$ and spin-orbit coupling leads to the following additional term in the Ginzburg-Landau functional [@edelstein_ginzburg_1996]: $$-\text{i}\,\varepsilon\,\vec{n}\cdot\left[\vec{h}\wedge\left(\Delta^{\star}\vec{\nabla}\Delta - \Delta\vec{\nabla}\Delta^{\star}\right)\right]  \, ,
\label{GL}$$ where $\vec{n}$ is a unit vector along the asymmetric potential gradient and the phenomelological constant $\varepsilon$ is proportional to the microscopic spin-orbit coupling constant $\alpha$. In the following, we will use the constant $\alpha$, defined below in Eq. (\[H\]), to characterize the spin orbit coupling strength. The term Eq. (\[GL\]) is always non-zero if the direction of the field $\vec{h}$ does not coincide with the direction of the spin-orbit vector $\vec{n}$ and may result in the formation of the modulated state with finite $\vec{q}$. This has been theoretically studied in several works 