Spin signature of Majorana zero modes in a Shiba chain

We propose as a robust and definite spin signature to distinguish Majorana zero modes from trivial Shiba states accidentally tuned to zero energy due to strong local potential. This signature is rooted in two sum rules that dictate the distribution of spin densities in a superconducting state with respect to a normal state, and can be straightforwardly detected with the spin-polarized scanning tunneling microscope technique which implicitly takes advantage of these sum rules.