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An unusual form of superconductivity, called Ising superconductivity, hasrecently been uncovered in mono- and few-layered transition metaldichalcogenides. This 2D superconducting state is characterized by theso-called Ising spin-orbit coupling (SOC), which produces strong oppositelyoriented effective Zeeman fields perpendicular to the 2D layer in oppositemomentum space valleys. We examine the Yu-Shiba-Rusinov (YSR) bound stateslocalized at magnetic impurities in Ising superconductors and show that theunusual SOC manifests itself in unusually strong anisotropy in magnetic fieldresponse of zero bias conductance peaks observable in STM experiments onimpurity sites. For a chain of magnetic impurities with moments parallel to theplane of Ising superconductors we show that the low energy YSR band can hosttopological superconductivity and Majorana fermions as a direct manifestationof Ising spin-orbit coupling induced topological effects.

Yu-Shiba-Rusinov states and topological superconductivity in Ising paired superconductors