Inhomogeneous stripe phase revisited for surface superconductivity.

We consider 2D surface superconductivity in high magnetic fields parallel to the surface. We demonstrate that the spin-orbit interaction at the surface changes the properties of the inhomogeneous superconducting Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state that develops above fields given by the paramagnetic criterion. Strong spin-orbit interaction significantly broadens the range of existence of the LOFF phase, which takes the form of periodic superconducting stripes running along the field direction on the surface, leading to the anisotropy of its properties. Our results provide a tool for studying surface superconductivity as a function of doping.