Spontaneous Spin Accumulation in Singlet-Triplet Josephson Junctions

We study the Andreev bound states in a Josephson junction between a singlet and a triplet superconductors. Because of the mismatch in the spin symmetries of pairing, the energies of the spin-up and -down quasiparticles are generally different. This results in imbalance of spin populations and net spin accumulation at the junction in equilibrium. This effect can be detected using probes of local magnetic field, such as the scanning SQUID, Hall, and Kerr probes. It may help to identify potential triplet pairing in $(\mathrm{TMTSF}{)}_{2}X$, ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, and oxypnictides.

Figure 1

A Josephson junction between a single and a triplet superconductors. The thin black solid lines represent chains for $(\mathrm{TMTSF}{)}_{2}X$ or planes for ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. The blue dotted lines indicates the localization lengths of the Andreev bound states. The cone represents a probe of the local magnetic field produced by spin accumulation at the interface.

Figure 2

(a) The energies $E_{\uparrow }$ (dashed lines) and $E_{\downarrow }$ (solid lines) of the Andreev bound states vs the phase ${\varphi }_0$ between the $s$ and $p_x$-wave superconductors ($D=0.8$ and ${\Delta }_2=0.5{\Delta }_1$). (b) Magnetic moment $m_z$ per unit area of the interface, Eq. (12), vs ${\varphi }_0$ for $T/{\Delta }_2=0.01$ (solid line) and 1 (dashed line).

Figure 3

The energies $E_{\uparrow }(k_y)$ (blue dotted lines) and $E_{\downarrow }(k_y)$ (red dash-dotted lines) vs $k_y$ for the phase ${\varphi }_0=\pi /2$ between the $s$ and $p_x+i{p}_y$ superconductors ($Z_0=1$). For ${\varphi }_0=0$ and $\pi$, $E_{\uparrow }(k_y)=E_{\downarrow }(k_y)$ is shown by the black solid line.

Figure 4

Normalized magnetic moment $m_z$ per unit area of the interface, Eq. (13), vs ${\varphi }_0$ for $T=0.01{\Delta }_2$ (solid line) and $T={\Delta }_2$ (dashed line) for a junction between the $s$ and $p_x+i{p}_y$ superconductors ($\rho =k_F/2\pi c$).