Disorder-robust $p$-wave pairing with odd frequency dependence in normal metal-conventional superconductor junctions

We investigate the induced superconducting pair correlations in junctions between a conventional spin-singlet $s$-wave superconductor and a disordered normal metal. Decomposing the pair amplitude based on its symmetries in the time domain, we demonstrate that the odd-time, or equivalently odd-frequency, spin-singlet $p$-wave correlations are both significant in size and entirely robust against random non-magnetic disorder. We find that these odd-frequency correlations can even be generated by disorder. Our results show that anisotropic odd-frequency pairing represent an important fraction of the proximity-induced correlations in disordered superconducting hybrid structures.