Orbitally limited pair-density wave phase of multilayer superconductors

TL;DR

This paper explores the conditions under which a pair-density wave phase appears in multilayer superconductors with Rashba spin-orbit coupling, revealing it stabilizes at high Maki parameters above 10.

Contribution

The study extends the circular cell Ginzburg-Landau method to include paramagnetic effects and identifies the minimal Maki parameter for pair-density wave stability in trilayer systems.

Findings

Pair-density wave phase stabilizes at Maki parameter > 10.

Rashba spin-orbit interaction influences phase stability.

First-order transition separates BCS and pair-density wave phases.

Abstract

We investigate the magnetic field dependence of an ideal superconducting vortex lattice in the parity-mixed pair-density wave phase of multilayer superconductors within a circular cell Ginzburg-Landau approach. In multilayer systems, due to local inversion symmetry breaking, a Rashba spin-orbit coupling is induced at the outer layers. This combined with a perpendicular paramagnetic (Pauli) limiting magnetic field stabilizes a staggered layer dependent pair-density wave phase in the superconducting singlet channel. The high-field pair-density wave phase is separated from the low-field BCS phase by a first-order phase transition. The motivating guiding question in this paper is: what is the minimal necessary Maki parameter $\alpha_M$ for the appearance of the pair-density wave phase of a superconducting trilayer system? To address this problem we generalize the circular cell method for the regular flux-line lattice of a type-II superconductor to include paramagnetic depairing effects. Then, we apply the model to the trilayer system, where each of the layers are characterized by Ginzburg-Landau parameter $\kappa_0$, and a Maki parameter $\alpha_M$. We find that when the spin-orbit Rashba interaction compares to the superconducting condensation energy, the orbitally limited pair-density wave phase stabilizes for Maki parameters $\alpha_M> 10$.