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Pair-density wave states through spin-orbit coupling in multilayer superconductors

Spin singlet superconductors with quasi-two dimensional multilayer structure are studied in high magnetic fields. Specifically we concentrate on bi- and tri-layer systems whose layers by symmetry are subject Rashba-type spin-orbit coupling. The combination of magnetic field and spin-orbit coupling leads to a first order phase transition between different states of layer-dependent superconducting order parameters upon rising the magnetic field. In this context we distinguish the low-field Bardeen-Cooper-Schrieffer state where all layers have order parameters of the same sign and the high-field pair-density wave state where the layer-dependent order parameters change the sign at the center layer. We also show that progressive paramagnetic limiting effects yield additional features in the H-T phase diagram. As possible realizations of such unusual superconducting phases we consider artificial superlattices of CeCoIn_5, as well as some multilayer high-T_c cuprates.