Andreev reflection from noncentrosymmetric superconductors and Majorana bound-state generation in half-metallic ferromagnets

We study Andreev reflection at an interface between a half metal and a superconductor with spin-orbit interaction. While the absence of minority carriers in the half metal makes singlet Andreev reflection impossible, the spin-orbit interaction gives rise to triplet Andreev reflection (i.e., the reflection of a majority electron into a majority hole or vice versa). As an application of our calculation, we consider a thin half-metal film or wire laterally attached to a superconducting contact. If the half metal is disorder free, an excitation gap is opened that is proportional to the spin-orbit interaction strength in the superconductor. For electrons with energy below this gap a lateral half-metal–superconductor contact becomes a perfect triplet Andreev reflector. We show that the system supports localized Majorana end states in this limit.

Figure 1

(a) Interface between a half metal (H ) and a superconductor (S). For a superconductor with spin-orbit scattering, normal reflection as well as triplet Andreev reflection—the reflection of a majority electron (e) into a majority hole (h)—take place at the HS interface. (b) A lateral contact between a half-metallic film or wire of thickness $d$ and a superconductor. For a lateral contact, an effective Andreev reflection amplitude $r_{\mathrm{he}}^{\mathrm{eff}}$ for electrons moving toward the contact region can be defined, which describes the combined effect of multiple reflections at the H S interface.

Figure 2

(a) Serial and (b) a lateral superconductor–half-metal–superconductor (SHS) junction.

Figure 3

A lateral contact between a half-metallic film or wire and a superconductor. The contact has length $L$, with a segment of length $\delta L$ singled out. The main text describes how the effective Andreev reflection of the entire lateral contact is calculated, starting from the effective Andreev reflection amplitudes ${\rho }_{\mathrm{he}}\delta L$ and ${\rho }_{\mathrm{eh}}\delta L$ of the segment of length $\delta L$. As discussed in Sec. 6, inserting a normally reflecting boundary at the left end of the H film or wire gives rise to a Majorana bound state.