Detailed theory of phase diagram of clean 2D surface superconductor in a
parallel magnetic field is presented. Regular spin-orbital interaction of the
Rashba type is known to produce inhomogeneous superconductive state similar to
the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state with Δ(r)∝cos(Qr) at high magnetic fields, with Q∼gμBh/vF. We
consider the case of relatively strong Rashba interaction and show that at low
temperatures T≤0.4Tc0 the LOFF-type state is separated from the usual
homogeneous state by the first-order phase transition line. At higher
temperatures new "helical" state with Δ(r)∝exp(iQr)
intervene between uniform BCS state and LOFF-like state. One component of
superfluid density tensor ns vanishes on the second-order transition line
between BCS state and helical state. Nonmagnetic impurities suppresses both
inhomogeneous states, and eliminate them completely at Tc0τ≤0.11.Comment: 5 pages, 1 figure; v2: as published, minor correction