Magnetic impurities as hosts of odd-frequency superconductivity

Odd-frequency (odd-ω) superconductivity is an example of unconventional dynamical order, where the Cooper pair correlations are both non-local and odd in relative time. Historically, the most important role regarding proximity-induced odd-ω pairing was played by superconductor-ferromagnet heterostructures. Shrinking the magnetic domain of this setup to the extreme, we demonstrate that all the necessary ingredients for generating odd-ω pairing are present in the vicinity of a paramagnetic impurity embedded in a conventional single-band bulk spin-singlet s-wave superconductor. We investigate the appearance of all possible pair amplitudes in accordance with the Berezinskii SPOT = -1 rule, which in our single-orbital case, trivially has O = +1. We study the spatial and frequency dependence of components classified by spatial parity, their evolution with impurity strength, and identify a reciprocity between different symmetries related through impurity scattering. We present calculations of physically measurable observables, such as spin-polarized local density of states, local spin susceptibility that carry signatures of odd-ω in some of their features.