Ferromagnetic chains grown on top of conventional superconductors (or, Yu-Shiba-Rusinov (YSR) chains) pose an interesting and promising platform for Majorana zero modes, which in turn is crucial in realizing feasible topological quantum computation. In this talk, I will first review the recent experimental and theoretical development of the study of Majorana zero modes in this platform [1,2,3,4]. Then I will propose a robust 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 has been recently detected with the spin-polarized scanning tunneling microscope technique which implicitly takes advantage of these sum rules [5,6].
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