  Semiconducting nanowires with strong spin-orbit coupling in the presence of
induced superconductivity and ferromagnetism can support Majorana zero modes.
We study the pumping due to the precession of the magnetization in
single-subband nanowires and show that spin pumping is robustly quantized when
the hybrid nanowire is in the topologically nontrivial phase, whereas charge
pumping is not quantized. Moreover, there exists one-to-one correspondence
between the quantized conductance, entropy change and spin pumping in long
topologically nontrivial nanowires but these observables are uncorrelated in
the case of accidental zero-energy Andreev bound states in the trivial phase.
Thus, we conclude that observation of correlated and quantized peaks in the
conductance, entropy change and spin pumping would provide strong evidence of
Majorana zero modes, and we elaborate how topological Majorana zero modes can
be distinguished from quasi-Majorana modes potentially created by a smooth
tunnel barrier at the lead-nanowire interface. Finally, we discuss peculiar
interference effects affecting the spin pumping in short nanowires at very low
energies.

Mesoscale and Nanoscale Physics