Phase diagram of a surface superconductor in parallel magnetic field

The universal phase diagram of a 2D surface superconductor with generic Rashba interaction in a parallel magnetic field is found. In addition to the uniform BCS state, we find two inhomogeneous superconductive states, the stripe phase with Δ ( r ) ∝ cos( Qr ) at high magnetic fields, and a new “helical” phase with Δ( r ) ∝ exp( i Qr ) which intervenes between the BCS state and stripe phase at an intermediate magnetic field and temperature. We prove that the ground state for helical phase carries no current.