Surface Bound States and Spin Currents in Noncentrosymmetric Superconductors

We investigate the ground state properties of a noncentrosymmetric superconductor near a surface. We determine the spectrum of Andreev bound states due to surface-induced mixing of bands with opposite spin helicities for a Rashba-type spin-orbit coupling. We find that the order parameter suppression qualitatively changes the bound state spectrum. The spin structure of Andreev states leads to a spin supercurrent along the interface, which is strongly enhanced compared to the normal state spin current. Particle and hole coherence amplitudes show Faraday-like rotations of the spin along quasiparticle trajectories.

Figure 1

A map of the spin-orbit vector in momentum space for the Rashba form ${\mathbf{g}}_{\mathbf{k}}=\widehat{\mathbf{k}}\times \widehat{\mathbf{z}}$. On reflection the spin-orbit vector ${\mathbf{g}}_{\mathbf{k}}$ may change, e.g., from $A\to A^{\prime }$, or not, $B\to B^{\prime }$. The scattering geometry is shown on the left.

Figure 2

Bound state energy as a function of the impact angle for different widths $W$ (in units of $v_f/2{\Delta }_0$) of the order parameter suppression region. Dark (light) lines correspond to the plus (minus) sign in Eq. (8). Solid lines: principal mode; broken lines: higher multiple reflection modes.

Figure 3

Structure of the surface states for a Rashba triplet superconductor (${\Delta }_{+}=-{\Delta }_{-}$). (a) Order parameter suppression; (b) DOS at locations indicated in (a); the large subgap peaks are due to the suppression of $\Delta$. Inset: DOS for a homogeneous order parameter; note the absence of any subgap features. (c, d) Spin-resolved surface DOS for two trajectories; $N_{\uparrow }(ϵ,{\mathbf{k}}_f)$ (dark) and $N_{\downarrow }(ϵ,{\mathbf{k}}_f)$ (light) correspond to dark and light branches in Fig. 2.

Figure 4

Spin currents near the surface. Left: Rashba metal. The nonvanishing components in the bulk are ${\Pi }_x^Y=-{\Pi }_y^X$. Near the surface ${\Pi }_y^Z$ is large; see text. Right: Spin currents and the order parameter in the SC state.