Josephson current and Andreev states in superconductor–half metal–superconductor heterostructures

We develop a detailed microscopic theory describing dc Josephson effect and Andreev bound states in superconducting junctions with a half metal. In such systems, the supercurrent is caused by triplet pairing states emerging due to spin-flip scattering at the interfaces between superconducting electrodes and the half metal. For sufficiently clean metals, we provide a detailed nonperturbative description of the Josephson current at arbitrary transmissions and spin-flip scattering parameters for both interfaces. Our analysis demonstrates that the behavior of both the Josephson current and Andreev bound states crucially depends on the strength of spin-flip scattering, showing a rich variety of features which can be tested in future experiments.

Figure 1

SNS junction and Riccati amplitudes in the clean limit. The functions ${\gamma }_i$, ${\Gamma }_i$ and ${\tilde{\gamma }}_i$, ${\tilde{\Gamma }}_i$ are Riccati amplitudes at the corresponding NS interface. ${\gamma }_{\pm }$ and ${\tilde{\gamma }}_{\pm }$ are Riccati amplitudes in the middle of the normal metal layer. Quasiparticle momentum directions are indicated by arrows.

Figure 2

(Color online) Phase dependence of the Josephson current at low temperatures and different spin-flip factors $\beta$. For simplicity, we consider the case of identical interfaces and assume that scattering parameters $\nu$, $\beta$, $\alpha$, and $\zeta$ are momentum independent. Parameter $\alpha$ is chosen to be real. The phase coherence length ${\xi }_0$ is defined as ${\xi }_0=v_F∕\left(2\pi T_c\right)$.

Figure 3

(Color online) Critical Josephson current $I_c$ as a function of temperature for different spin-flip factors $\beta$. The inset shows the current-phase relation for ${\beta }_1={\beta }_2=0.99$ and at temperatures $T∕T_c=0.01$ (solid line), 0.1 (dashed line), 0.2 (dotted line). For simplicity, we consider the case of identical interfaces and assume that scattering parameters $\nu$, $\beta$, $\alpha$, and $\zeta$ are momentum independent. Parameter $\alpha$ is chosen to be real.

Figure 4

The function $F\left(\phi \right)$ defined in Eq. (86).

Figure 5

The higher and lower Andreev levels in short SHS junctions with highly transparent interfaces for $\mid {\beta }_1\mid =\mid {\beta }_2\mid =0.8$.

Figure 6

The same as in Fig. 5 for $\mid {\beta }_1\mid =\mid {\beta }_2\mid =0.2$.

Figure 7

The structure of Andreev bound states in short SHS junctions with highly transparent interfaces for $\mid {\beta }_1\mid =\mid {\beta }_2\mid =0.8$ (upper figure) and $\mid {\beta }_1\mid =\mid {\beta }_2\mid =0.2$ (lower figure) at $\phi =2.5$.