Spin diagnostics for Majorana zero modes in a Yu-Shiba-Rusinov chain

In the first part of this talk, I will briefly review the recent development of the study of Majorana zero modes in magnetic chains grown on top of conventional superconductors [or, Yu-Shiba-Rusinov (YSR) chains]. In the second part, I will propose a robust and definite spin signature to distinguish Majorana zero modes from trivial YSR 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.