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 trilayer systems whose layers by symmetry are subject to 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 raising 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 ${\mathrm{CeCoIn}}_{5}$ as well as some multilayer high-${T}_{\mathrm{c}}$ cuprates.