Theory of 2D superconductor with broken inversion symmetry

Abstract

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 $T\le 0.4T_{c0}$ 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 $\Delta (r)\propto \exp (iQr)$ intervenes between the uniform BCS state and the LOFF-like state at $g{\mu }_{B}h\approx 1.5T_{c0}$. 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 $T_{c0}\tau \le 0.11$. 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.

23 pages, 14 figures

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