Theory of a two-dimensional superconductor with broken inversion symmetry

A detailed theory of a phase diagram of a 2D surface superconductor in a parallel magnetic field is presented. A spin-orbital interaction of the Rashba type is known to produce at a high magnetic field $h$ (and in the absence of impurities) an inhomogeneous superconductive phase similar to the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state with an order parameter $\Delta(r) \propto \cos(Qr)$. We consider the case of a strong Rashba interaction with the spin-orbital splitting much larger than the superconductive gap $\Delta$, and show that at low temperatures $T\leq 0.4 T_{c0}$ the LOFF-type state is separated from the usual homogeneous state by a first-order phase transition line. At higher temperatures another inhomogeneous state with $\Delta(r) \propto \exp(i Qr)$ intervenes between the uniform BCS state and the LOFF-like state at $g\mu_B h \approx 1.5 T_{c0}$. The modulation vector $Q$ in both phases is of the order of $g\mu_B h/v_F$. The superfluid density $n_s^{yy}$ vanishes in the region around the second-order transition line between the BCS state and the new ``helical'' state. Non-magnetic impurities suppress both inhomogeneous states, and eliminate them completely at $T_{c0}\tau \leq 0.11$. However, once an account is made of the next-order term over the small parameter $\alpha/v_F \ll 1$, a relatively long-wave helical modulation with $Q \sim g\mu_B h\alpha/v_F^2$ is found to develop from the BCS state. This long-wave modulation is stable with respect to disorder. In addition, we predict that unusual vortex defects with a continuous core exist near the phase boundary between the helical and the LOFF-like states. In particular, in the LOFF-like state these defects may carry a half-integer flux.