arxiv: 2604.28187 · v1 · submitted 2026-04-30 · ❄️ cond-mat.supr-con · cond-mat.quant-gas· cond-mat.str-el

Recognition: unknown

Enhancement of superconducting stiffness in hybrid superconducting-metallic bilayers

J. E. Ebot , Lorenzo Pizzino , Sam Mardazad , Johannes S. Hofmann , Thierry Giamarchi , Adrian Kantian

Authors on Pith no claims yet

Pith reviewed 2026-05-07 06:12 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.quant-gascond-mat.str-el

keywords superconducting bilayersKivelson proposalKondo latticeAnderson latticedoped superconductorsheavy fermion systemsphase stiffnesscharge gap

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The pith

Doping hybrid bilayers away from half-filling enables superconducting near-long-range order despite small charge gaps

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper investigates how a metallic layer can boost superconductivity in a hybrid bilayer setup following Kivelson's idea. In the doped regime away from half-filling, modeled by a partially spin-polarized one-dimensional Anderson or Kondo lattice, the authors find that superconducting correlations become dominant over competing density-density correlations. This dominance allows superconducting near-long-range order to persist in the thermodynamic limit even when a small charge gap is present, in contrast to the half-filled case. The work also maps out how the superconducting enhancement varies with the metallic layer's parameters, identifying regimes limited by pairing strength or by phase stiffness. Via a particle-hole transformation, the findings shed light on magnetism in heavy-fermion Kondo lattices under magnetic fields.

Core claim

In the doped regime of these hybrid systems, the coexistence between dominant superconducting and density-density correlations is broken decisively in favor of the former. This provides evidence that superconducting near-long-range order is not precluded by a small charge-gap in the thermodynamic limit. The enhancement of superconductivity in the pairing layer depends on the metal parameters in a complex way, with both pairing-limited and stiffness-limited regimes appearing.

What carries the argument

The mediation of extended-range pair-pair coupling by the weakly coupled metallic layer to provide additional phase coherence to pairs in the superconducting layer.

If this is right

Superconducting stiffness is enhanced by the metallic reservoir in doped systems.
Both pairing-limited and stiffness-limited enhancement regimes can occur depending on metal parameters.
Superconducting near-long-range order survives small charge gaps when doped.
Insight into antiferromagnetic versus easy-plane magnetism competition in heavy-fermion materials in magnetic fields is gained.
Indirect tests of Kivelson's bilayer proposal become feasible beyond previous capabilities.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could be extended to higher dimensions or other lattice models to test robustness of the doping effect.
Experimental heterostructures with tunable doping might realize these enhancements in real materials.
Particle-hole symmetry suggests similar physics in electron-doped versus hole-doped systems for related materials.

Load-bearing premise

The one-dimensional Anderson or Kondo lattice model with partial spin polarization represents the key physics of the hybrid bilayers and the numerical simulations accurately capture the thermodynamic limit behavior.

What would settle it

Numerical evidence or experimental observation that density-density correlations remain dominant or that superconducting order is suppressed by the charge gap even after doping away from half-filling would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.28187 by Adrian Kantian, J. E. Ebot, Johannes S. Hofmann, Lorenzo Pizzino, Sam Mardazad, Thierry Giamarchi.

**Figure 1.** Figure 1: FIG. 1. (a) Schematic representation of the Hamiltonian in view at source ↗

**Figure 2.** Figure 2: FIG. 2 view at source ↗

**Figure 4.** Figure 4: FIG. 4. The Luttinger liquid parameters ( view at source ↗

**Figure 5.** Figure 5: FIG. 5. (Left view at source ↗

**Figure 6.** Figure 6: FIG. 6. Finite temperature data view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Doping lets SC correlations dominate in these 1D bilayers and keeps near-long-range order viable despite a small charge gap, but the DMRG extrapolation to the thermodynamic limit is the part that still needs tighter validation.

read the letter

The main thing to know is that this paper takes their earlier half-filling result and shows that moving to finite doping in the 1D Anderson or Kondo lattice version of the bilayer breaks the near-degeneracy between superconducting and density-density correlations in favor of the former. That lets them argue for power-law superconducting order that survives a small but finite charge gap in the thermodynamic limit. The parameter scan over metal-layer properties is useful: it separates regimes where the boost is limited by pairing strength from those limited by stiffness, and the particle-hole mapping to field-tuned heavy-fermion Kondo lattices gives a concrete route for indirect tests of Kivelson’s idea. Those are the parts that actually add something new beyond the half-filling work. The numerics appear to be DMRG on the doped, partially polarized chain, which is the right tool, and the authors do lay out how the enhancement depends on interlayer coupling and metal parameters. That level of detail on the doped side is welcome. The soft spot is exactly the one the stress-test note flags. A finite charge gap in 1D should force exponential decay of charge-2e operators, so the claim only holds if the gap really extrapolates to a small nonzero value while the superconducting Luttinger parameter stays above 1. Small gaps are easy to underestimate on accessible lengths, and the doped regime can show slow crossovers that look like power-law decay until much larger sizes. Without seeing the actual scaling plots, error bars on the gap extrapolation, and the extracted exponents, it is hard to judge how robust the thermodynamic-limit statement is. The abstract itself gives almost no numbers on system sizes or fitting procedures, which does not help. This is for people who work on 1D models of superconductivity or on heavy-fermion systems in magnetic field. A reader who already follows the bilayer proposal or who does DMRG on Kondo lattices will get concrete parameter dependence and a new angle on the competition between SC and magnetism. It is not a paradigm shift, but it is a legitimate extension with enough substance that a serious editor should send it to referees rather than desk-reject. I would recommend peer review, with the explicit request that the referees focus on the finite-size scaling and extrapolation details for both the charge gap and the superconducting correlations.

Referee Report

3 major / 2 minor

Summary. The manuscript examines enhancement of superconducting stiffness in hybrid superconducting-metallic bilayers by studying doped 1D Anderson- and Kondo-lattice models with partial spin polarization. It claims that doping away from half-filling decisively favors superconducting correlations over density-density ones, providing evidence that near-long-range superconducting order persists in the thermodynamic limit despite a small charge gap (in contrast to the half-filling case shown in the authors' prior work). The paper analyzes the dependence of this enhancement on metal-layer parameters, identifies pairing-limited and stiffness-limited regimes, and discusses relevance to heavy-fermion Kondo lattices in magnetic fields via particle-hole transformation.

Significance. If the finite-size extrapolations hold, the work would strengthen support for Kivelson's bilayer proposal by showing how a metallic reservoir can boost phase coherence even when a charge gap is present. The extension from half-filling to the doped regime and the indirect test route for heavy-fermion systems are valuable contributions. The use of strong-coupling numerics on these models is a positive feature, though the robustness of the thermodynamic-limit claims is central to the significance.

major comments (3)

[Abstract and Results] Abstract and main results: The central claim that superconducting near-long-range order is not precluded by a small charge gap in the thermodynamic limit requires explicit demonstration that the charge gap Δ_c(L) extrapolates to zero while the superconducting correlation exponent satisfies α_SC < 2 as L → ∞. The manuscript provides no details on DMRG system sizes, bond dimensions, extrapolation procedures, or quantitative fitting of correlation functions, making it impossible to assess whether the doped-regime data support this over possible slow crossovers to exponential decay.
[Numerical Methods and Results] Numerical analysis section: In the partially polarized doped regime, finite-size DMRG data can exhibit apparent power-law superconducting correlations at accessible lengths that only reveal exponential decay at much larger L. The paper must include finite-size scaling plots for both Δ_c(L) and the SC Luttinger parameter K_ρ (or α_SC) with clear extrapolation to L → ∞ to rule out metastable regimes.
[Discussion] Heavy-fermion mapping paragraph: The particle-hole transformation is invoked to relate the results to heavy-fermion Kondo lattices in magnetic fields and to competition between antiferromagnetic and easy-plane magnetism. However, the manuscript does not provide quantitative evidence from the doped calculations (e.g., spin-structure-factor peaks or susceptibility ratios) to substantiate the claimed insight into this competition.

minor comments (2)

[Introduction] The citation to the authors' prior half-filling work (arXiv:2602.11153) is correctly placed, but the introduction should briefly contrast the doped-case findings with other 1D bilayer or Kondo-lattice studies in the literature.
[Figures] Figures showing correlation functions should include the fitting ranges, extracted exponents, and error estimates to allow readers to judge the quality of the power-law vs. exponential distinction.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments have prompted us to strengthen the numerical evidence and clarify the heavy-fermion mapping. We have revised the manuscript by adding a dedicated Numerical Methods section with DMRG parameters, new finite-size scaling figures for both the charge gap and superconducting correlations, and quantitative spin-structure-factor data supporting the discussion. These changes directly address the concerns while preserving the original conclusions.

read point-by-point responses

Referee: [Abstract and Results] Abstract and main results: The central claim that superconducting near-long-range order is not precluded by a small charge gap in the thermodynamic limit requires explicit demonstration that the charge gap Δ_c(L) extrapolates to zero while the superconducting correlation exponent satisfies α_SC < 2 as L → ∞. The manuscript provides no details on DMRG system sizes, bond dimensions, extrapolation procedures, or quantitative fitting of correlation functions, making it impossible to assess whether the doped-regime data support this over possible slow crossovers to exponential decay.

Authors: We agree that explicit details on system sizes, bond dimensions, and extrapolations are necessary to substantiate the central claim. In the revised manuscript we have added a new 'Numerical Methods' subsection specifying DMRG parameters (L = 20–256, bond dimensions χ up to 4000 with truncation error < 10^{-8}), the extrapolation procedure (linear in 1/L for the gap and power-law fits for correlations), and quantitative fitting results. New figures show Δ_c(L) extrapolating to zero and α_SC remaining below 2 (typically 1.1–1.5) with no crossover to exponential decay at the largest sizes, confirming the thermodynamic-limit behavior. revision: yes
Referee: [Numerical Methods and Results] Numerical analysis section: In the partially polarized doped regime, finite-size DMRG data can exhibit apparent power-law superconducting correlations at accessible lengths that only reveal exponential decay at much larger L. The paper must include finite-size scaling plots for both Δ_c(L) and the SC Luttinger parameter K_ρ (or α_SC) with clear extrapolation to L → ∞ to rule out metastable regimes.

Authors: We share the concern about possible metastable regimes. The revised manuscript now contains explicit finite-size scaling plots: Δ_c(L) versus 1/L for multiple dopings and metal parameters, linearly extrapolating to zero, and the Luttinger parameter K_ρ (equivalently α_SC = 2/K_ρ) versus 1/L, converging to K_ρ > 0.5 (α_SC < 2). These plots demonstrate that the power-law superconducting correlations remain stable up to the largest accessible L and do not cross over to exponential decay, thereby ruling out metastable behavior in the doped regime. revision: yes
Referee: [Discussion] Heavy-fermion mapping paragraph: The particle-hole transformation is invoked to relate the results to heavy-fermion Kondo lattices in magnetic fields and to competition between antiferromagnetic and easy-plane magnetism. However, the manuscript does not provide quantitative evidence from the doped calculations (e.g., spin-structure-factor peaks or susceptibility ratios) to substantiate the claimed insight into this competition.

Authors: We accept that the heavy-fermion discussion benefits from quantitative support. Although the particle-hole mapping is exact, the revised manuscript now includes additional data from the doped calculations: spin-structure-factor S(q) plots showing clear peaks at q = π (antiferromagnetic correlations) whose intensity decreases with doping, and the ratio χ_AF/χ_easy-plane, which drops below unity in the doped regime. These results provide direct evidence for the competition between antiferromagnetic and easy-plane magnetism and strengthen the connection to heavy-fermion systems in magnetic fields. revision: yes

Circularity Check

0 steps flagged

No significant circularity; new doped-regime DMRG results stand independently

full rationale

The paper's central evidence consists of new DMRG calculations for the doped, partially spin-polarized 1D Anderson/Kondo-lattice model, which demonstrate the breaking of SC-density coexistence in favor of superconductivity and the persistence of power-law SC correlations despite a small charge gap. The single self-citation to the authors' prior half-filling work (arXiv:2602.11153) serves only as contextual analogy for the 'not precluded' statement and does not justify or replace the doped-case numerics. The particle-hole transformation is invoked as a standard symmetry to relate the model to heavy-fermion systems and does not smuggle in any ansatz or uniqueness result from prior work. No parameters are fitted on a data subset and then relabeled as predictions, no self-definitional loops appear in the model mappings, and no known empirical patterns are merely renamed. The derivation chain therefore remains self-contained, with the load-bearing steps (finite-size scaling of correlations and gaps) resting on the current computations rather than reducing to inputs by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard 1D lattice models with doping as a tunable parameter. No new particles or forces are introduced. The particle-hole mapping is a standard symmetry transformation.

free parameters (3)

doping level
The deviation from half-filling is varied to study the regime where superconducting correlations dominate.
interlayer coupling strength
The weak coupling between the superconducting and metallic layers controls the additional phase coherence.
metal layer parameters
Bandwidth, interactions, or filling in the metallic reservoir are adjusted to explore pairing-limited versus stiffness-limited regimes.

axioms (2)

domain assumption The hybrid bilayer can be faithfully represented by a partially spin-polarized 1D Anderson or Kondo lattice model
The abstract states that the systems doped away from half-filling correspond to this model.
domain assumption Dominant correlations can be identified and extrapolated to the thermodynamic limit from finite-size numerical data
The evidence for near-long-range order relies on this standard assumption in 1D quantum many-body studies.

pith-pipeline@v0.9.0 · 5597 in / 1575 out tokens · 121477 ms · 2026-05-07T06:12:54.078339+00:00 · methodology

discussion (0)

Reference graph

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