Control of Edge Currents at a Ferromagnet - Triplet Superconductor Interface by Multiple Helical Majorana Modes

We study the spin and charge currents flowing at the interface of an itinerant ferromagnet with a topological spin-triplet superconductor having different number of time-reversal-invariant Majorana helical modes. Depending on the number of helical modes, the capacity of carrying spin and charge currents is shown to be directly related to the amplitude and orientation of the ferromagnetic magnetization with respect to the superconducting $\vec{d}$-vector. Differently from the one-helical mode spin-triplet superconductor, we find that the presence of a finite amount of electronic hybridization with the two pairs of Majorana helical modes leads to nonvanishing charge current independently of the ferromagnetic exchange. The competition between the two pairs of Majorana helical modes remarkably yields a spin-current response that is almost constant in the range of weak to intermediate ferromagnetism. The behavior of the spin current is tightly linked to the direction of the spin-polarization in the ferromagnet and tends to be flatten for a magnetization that is coplanar to the spin-triplet $\vec{d}$-vector independently of the number of helical modes.