Oscillatory superconducting transition temperature in superconductor/antiferromagnet heterostructures

One of the most famous proximity effects at ferromagnet/superconductor (FM/SC) interfaces is partial conversion of singlet superconductivity to triplet pairing correlations. Due to the presence of macroscopic exchange field in the ferromagnet the Cooper pairs penetrating into the ferromagnet from the superconductor acquire a finite momentum there. The finite-momentum pairing manifests itself, in particular, as a nonmonotonic dependence of the critical temperature of the bilayer on the thickness of the FM layer. Here we predict that despite the absence of the macroscopic exchange field the critical temperature of the antiferromagnet/superconductor (AFM/SC) bilayers also exhibit nonmonotonic (oscillating) dependence on the AFM layer thickness. It is a manifestation of the proximity-induced N\'eel-type triplet correlations, which acquire finite total pair momentum and oscillate in the AFM layer due to the Umklapp electron-scattering processes at the AFM/SC interface. Our prediction can provide a possible explanation for a number of recently published experimental observations of the critical temperature of AFM/SC bilayers.