Enhancement of superconducting stiffness in hybrid superconducting-metallic bilayers

TL;DR

This study investigates how metallic reservoirs enhance superconducting stiffness in bilayer systems, especially when doped away from half-filling, revealing regimes where superconductivity is significantly improved.

Contribution

The paper provides new insights into the doping-dependent enhancement of superconductivity in bilayers, demonstrating regimes where superconducting order is robust despite small charge gaps.

Findings

Superconducting near-long-range order persists in doped regimes.

Both pairing-limited and stiffness-limited regimes can occur.

Results are relevant for heavy-fermion Kondo-lattice materials.

Abstract

Boosting superconductivity by metallic reservoirs is the essence of Kivelson's bilayer proposal. One layer provides pairing to the electrons, while the weakly coupled metal provides additional phase coherence to those pairs by mediating extended-range pair-pair coupling. Demonstrating significant and unambiguous performance gains with strong-coupling methods for such set-ups had been difficult. In the present work, we study these systems doped away from half-filling, corresponding to a partially spin-polarized 1D Anderson- or Kondo-lattice. We show that this breaks the coexistence of dominant superconducting and density-density correlations decisively in favour or the former. Consequently, we provide evidence that in this doped regime, superconducting near-long-range order is not precluded by a small charge-gap in the thermodynamic limit, as we have recently shown to be the case at half-filling [JE Ebot $et$ $al.$, arXiv:2602.11153 [cond-mat.supr-con]]. We study the complex manner in which the enhancement of superconductivity in the pairing layer depends on the parameters of the metal, and especially that both pairing-limited and stiffness-limited regimes may appear in these systems. In addition to superconducting bilayers, our results are relevant, via a particle-hole transformation, for heavy-fermion Kondo-lattice materials in magnetic fields, as we provide previously lacking insight on the competition between antiferromagnetic and easy-plane magnetism, as well as a route for comprehensive indirect tests of Kivelson's bilayer proposal well beyond previous capabilities.