Spin Current due to Spinlike Andreev Reflection

We propose theoretically a spinlike Andreev reflection that may occur at the interface of a semimetal and a doped excitonic insulator. In contrast to the usual Andreev reflection, this process does not produce the charge current, but gives rise to a pure spin current. Further investigation reveals the existence of a spinlike Josephson phenomenon between two excitonic insulators with ferromagnetism, which results in a dissipationless spin current. We stress that the present spin current satisfies the conservation condition and is quite different from the spin Hall current induced from spin-orbital interactions.

Figure 1

(a) Charge Andreev refection process at the interface of a normal metal and a superconductor: A spin-up electron above the Fermi energy is reflected as a spin-up hole below the Fermi energy with a Cooper pair transferred to the superconductor. (b) Spinlike Andreev reflection process at the interface of a semimetal and an excitonic insulator with ferromagnetism $\overrightarrow{M}$: A spin-up electron in conducting band is reflected as a spin-down electron in valence band with a triplet electron-hole pair transferred to the excitonic insulator.

Figure 2

The spinlike Andreev reflection coefficient $T_A$ versus the energy $E$ for different values of the dimensionless parameters $\xi \equiv {\pi }^2{T}^2{D}_L{D}_R$.