Josephson Effect due to Odd-Frequency Pairs in Diffusive Half Metals

Motivated by a recent experiment [Keizer et al., Nature (London) 439, 825 (2006)], we study the Josephson effect in superconductor/diffusive half metal/superconductor junctions using the recursive Green function method. The spin-flip scattering at the junction interfaces opens the Josephson channel of the odd-frequency spin-triplet Cooper pairs. As a consequence, the local density of states in a half metal has a large peak at the Fermi energy. Therefore the odd-frequency pairs can be detected experimentally by using the scanning tunneling spectroscopy.

Figure 1

(a) A schematic figure of a SFS junction on the tight-binding lattice. (b) The density of states for each spin direction. The Josephson junction is of the SNS, SFS, and S/HM/S type for $V_{\mathrm{ex}}/t=0$, 1, and 2.5, respectively.

Figure 2

(a) The Josephson current versus the exchange potential $V_{\mathrm{ex}}$. At $V_{\mathrm{ex}}=2t$, a ferromagnet becomes half-metallic as indicated by an arrow. (b) The pairing function of spin-singlet pairs $⟨f_0⟩$ versus position $j$ for $V_{\mathrm{ex}}/t=0$ (SNS) and 2.5 (S/HM/S); (c) for $V_{\mathrm{ex}}/t=1$ (SFS). (d) The pairing function in three different samples for $V_{\mathrm{ex}}/t=1$, the vertical axis is offset by 0.5 as indicated by the horizontal lines. The spin-flip scattering is absent in all panels, $V_S=0$.

Figure 3

(a) The Josephson current and its fluctuations at $T=0.1T_c$ and $\phi =\frac{\pi }{2}$ as a function of the interface spin-flip scattering $V_S$ for $V_{\mathrm{ex}}/t=1$ and (b) for $V_{\mathrm{ex}}/t=2.5$. The pairing functions versus position $j$ in a ferromagnet (c) and in a half metal (d) at $V_s=0.4t$, $\phi =0$, and ${\omega }_n=0.02{\Delta }_0$. $⟨f_{\uparrow \uparrow }⟩$ and $⟨f_{\downarrow \downarrow }⟩$ are the pairing functions of equal spin pairs, and $\delta f_0\gg ⟨f_0⟩$ indicates the amplitude of pairing function for spin-singlet pairs.

Figure 4

(a) Dependences of the pairing functions on ${\omega }_n$. (b) The local density of states at $j=37$ in a half metal at $V_S=0.5t$ and in a normal metal at $V_S=0$.