Characterizing $p$-wave superconductivity using the spin structure of Shiba states

Cooper pairs in two-dimensional unconventional superconductors with broken inversion symmetry are in a mixture of an even-parity spin-singlet pairing state with an odd-parity spin-triplet pairing state. We study the magnetic properties of the impurity bound states in such superconductors and find striking signatures in their spin polarization which allow one to unambiguously discriminate a nontopological superconducting phase from a topological one. Moreover, we show how these properties, which could be measured using spin-polarized scanning tunneling microscopy (STM), also enable one to determine the direction of the spin-triplet pairing vector of the host material and thus to distinguish between different types of unconventional pairing.