Theory of topological spin current in noncentrosymmetric superconductors

We study the spin transport properties of the noncentrosymmetric superconductor with time-reversal symmetry where spin-triplet $\left(p_x\pm i{p}_y\right)$-wave and spin-singlet $s$-wave pair potentials can mix with each other. We show that when the amplitude of the $\left(p_x\pm i{p}_y\right)$-wave pair potential is larger than that of $s$-wave one, the superconducting state belongs to the topologically nontrivial class analogous to the quantum spin Hall system, and the resulting helical edge modes as Andreev bound states are topologically protected. We find that the incident angle dependent spin polarized current flows through the interface due to the presence of the helical edge modes. With a weak magnetic field, also the angle-integrated current is strongly spin polarized.

Figure 1

(Color online) Angle-resolved spin conductance for $Z=5$. a: $eV=0.1{\Delta }_p$, b: $eV=-0.1{\Delta }_p$, and c: $eV=0.6{\Delta }_p$, with $\lambda k_F=0.1\mu$. (a) Pure $\left(p_x\pm i{p}_y\right)$-wave case with ${\Delta }_s=0$. (b) ${\Delta }_s=0.3{\Delta }_p$.

Figure 2

(Color online) Angle averaged spin conductance ${\sigma }_S$ (left panel) and charge conductance ${\sigma }_C$ (right panel) as a function of $eV$ with bias voltage $V$ with $\lambda k_F=0.1\mu$. a: $H=0$, b: $H=0.2H_0$, c: $H=-0.2H_0$, and d: $H=0.4H_0$. Curves $b$ and $c$ of the right panel are identical.

Figure 3

(Color online) Angle averaged spin and charge conductance for $eV=0$ as a function of $H$ with $\lambda k_F=0.1\mu$. a: Spin conductance and b: charge conductance.