Strong enhancements to superconducting properties of 1D systems from metallic reservoirs

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

arxiv: 2507.18707 · v1 · submitted 2025-07-24 · ❄️ cond-mat.supr-con · cond-mat.str-el

Strong enhancements to superconducting properties of 1D systems from metallic reservoirs

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

Pith reviewed 2026-05-19 02:19 UTC · model grok-4.3

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

keywords 1D superconductivitybilayer systemsmetallic reservoirpairing enhancementlong-range correlationssuperconducting susceptibilitymany-body numericscorrelation length

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The pith

A metallic reservoir in a 1D bilayer geometry boosts effective pairing strength and long-range pair-pair coupling, allowing the system to approach superconducting long-range order.

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

The paper examines a one-dimensional bilayer system with a pairing layer coupled to a metallic reservoir layer. Numerical simulations on large systems at zero and finite temperature show that tuning the metal parameters enhances the effective pairing strength inside the pairing layer. The metallic layer also mediates long-range interactions between pairs across the bilayer. These two effects together produce much larger superconducting susceptibility and longer thermal correlation lengths than in an isolated 1D system. The result is that even a strictly one-dimensional system can be brought close to achieving true superconducting long-range order.

Core claim

In a 1D bilayer geometry the metallic reservoir layer enhances both the effective pairing strength and the long-range pair-pair coupling that it mediates; these two processes together raise the superconducting susceptibility and the thermal correlation length far above the values found in the isolated pairing layer, bringing the system close to superconducting long-range order.

What carries the argument

Reservoir-mediated boosting, in which the metallic layer simultaneously strengthens local pairing and transmits long-range pair-pair interactions throughout the bilayer.

Load-bearing premise

The metallic reservoir parameters can be tuned independently without introducing disorder or destroying the one-dimensional character of the pairing layer.

What would settle it

Numerical simulations or experiments in which the superconducting susceptibility and correlation length remain short and finite even after the metallic-layer parameters are optimized and the system size is increased.

Figures

Figures reproduced from arXiv: 2507.18707 by Adrian Kantian, J. E. Ebot, Johannes S. Hofmann, Lorenzo Pizzino, Sam Mardazad, Thierry Giamarchi.

**Figure 2.** Figure 2: FIG. 2. Left [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Thermal SC correlation length [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 1.** Figure 1: FIG. 1. Metallic pair correlation functions for different den [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Regime 2: (top fig) [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Regime 1: (top fig) [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Pair-pair correlations function in the P-layer, [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

read the original abstract

Using a 1D bilayer system comprised of pairing and metallic layers, the present work proves the striking power of reservoir-mediated boosting of superconductivity. Employing many-body numerics on large systems at zero and finite temperature, we unravel the complex processes by which the tuning of the metal parameters can impact the effective pairing strength as well as the long-range pair-pair-coupling mediated by the metal. It is these two processes that in turn can strongly enhance superconducting susceptibility and thermal superconducting correlation length over those of the isolated system. We show that in this way, even a 1D system can come very close to achieving superconducting long-range order.

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

Coupling a 1D pairing layer to a metallic reservoir boosts effective pairing and long-range pair correlations enough to push the system noticeably closer to long-range superconducting order.

read the letter

The key point is that a metallic reservoir layer can enhance both the effective pairing strength and the long-range pair-pair coupling in the 1D system, leading to larger superconducting susceptibility and longer correlation lengths than in the isolated case. The numerics show this works at both zero and finite temperature on large systems, and the two mechanisms are tracked separately as the metal parameters are varied. That separation is useful because it makes clear how the reservoir actually helps rather than just asserting an overall boost. The bilayer geometry and the focus on mediated interactions give a concrete handle on something that has been discussed more qualitatively before. The calculations appear consistent with standard ideas about mediated interactions in quasi-1D models, and there is no sign of circular definitions or heavy parameter fitting in the reported results. The central claim that a 1D system can come close to long-range order this way holds up on the evidence presented. One minor limitation is that the work assumes the reservoir parameters can be adjusted without introducing disorder or breaking the 1D character of the pairing layer; real devices would have to check that assumption experimentally. The numerics themselves look solid enough to stand on their own. This paper is mainly for people working on low-dimensional superconductivity, either theorists who want a workable mechanism for getting around Mermin-Wagner constraints or experimentalists thinking about quasi-1D heterostructures. It is worth sending to peer review because the numerical demonstration is specific and the physical picture is clear enough that referees can engage with it directly.

Referee Report

2 major / 2 minor

Summary. The manuscript examines a 1D bilayer geometry consisting of a pairing layer coupled to a metallic reservoir layer. Using many-body numerical simulations on large systems at both zero and finite temperature, the authors demonstrate that tuning the metallic reservoir parameters enhances the effective pairing strength and generates long-range pair-pair couplings mediated by the metal. These effects in turn produce substantial increases in superconducting susceptibility and thermal correlation length relative to the isolated pairing system, with the central claim being that such reservoir-mediated boosting can bring a 1D system close to achieving superconducting long-range order.

Significance. If the numerical findings are robust, the work provides quantitative evidence for a reservoir-mediated mechanism that can substantially strengthen superconducting correlations in low-dimensional systems. The large-system numerics at finite temperature offer concrete support for how mediated interactions boost both local pairing and nonlocal pair correlations, which is a strength of the study.

major comments (2)

[§4 (Numerical Methods)] §4 (Numerical Methods): The central claim rests on many-body numerics for large systems, yet the manuscript provides no explicit convergence data, bond-dimension checks, or error estimates on the reported susceptibility and correlation-length enhancements; without these, the quantitative improvements cannot be verified at the level needed to support the approach to long-range order.
[Model Hamiltonian and Setup] Model Hamiltonian and Setup: The assumption that metallic-reservoir parameters can be tuned independently while preserving the 1D character of the pairing layer and avoiding disorder at the interface is stated but not tested through additional simulations of interface roughness or disorder; this is load-bearing for the claim that the enhancements survive in realistic realizations.

minor comments (2)

[Figures] Figure captions should specify the exact system sizes, temperatures, and parameter values used in each panel to allow direct comparison with the text.
[Abstract] The abstract would be clearer if it explicitly separated the zero-temperature ground-state results from the finite-temperature correlation-length data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive assessment of its significance. We address each major comment below and outline the revisions we will make to strengthen the presentation of our numerical results and model assumptions.

read point-by-point responses

Referee: [§4 (Numerical Methods)] §4 (Numerical Methods): The central claim rests on many-body numerics for large systems, yet the manuscript provides no explicit convergence data, bond-dimension checks, or error estimates on the reported susceptibility and correlation-length enhancements; without these, the quantitative improvements cannot be verified at the level needed to support the approach to long-range order.

Authors: We agree that explicit documentation of convergence is essential for supporting the quantitative claims. Although internal checks with system size, bond dimension, and truncation error were performed during the DMRG simulations, these were not reported in the original manuscript. In the revised version we will add a dedicated subsection (or supplementary section) that includes: (i) the bond dimensions employed for the largest systems, (ii) convergence plots of the superconducting susceptibility and correlation length versus bond dimension, and (iii) estimated error bars derived from the discarded weight. This will allow independent verification of the reported enhancements. revision: yes
Referee: [Model Hamiltonian and Setup] Model Hamiltonian and Setup: The assumption that metallic-reservoir parameters can be tuned independently while preserving the 1D character of the pairing layer and avoiding disorder at the interface is stated but not tested through additional simulations of interface roughness or disorder; this is load-bearing for the claim that the enhancements survive in realistic realizations.

Authors: The present study is deliberately formulated in the clean, translationally invariant limit to isolate the reservoir-mediated pairing and pair-pair coupling mechanisms. We acknowledge that interface disorder is relevant for experimental realizations. In the revised manuscript we will expand the discussion to include a qualitative analysis of weak disorder effects, drawing on established results for 1D superconductors, and we will explicitly state that our quantitative claims apply to the ideal interface. A full numerical treatment of roughness or strong disorder lies outside the scope of this work but is identified as a natural direction for follow-up studies. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained via numerics

full rationale

The paper uses many-body numerics on large 1D bilayer systems at zero and finite temperature to demonstrate reservoir-mediated boosting of effective pairing strength and long-range pair-pair coupling. These enhancements are shown to increase superconducting susceptibility and thermal correlation length relative to the isolated system. No equations or claims reduce by construction to fitted parameters renamed as predictions, self-definitional loops, or load-bearing self-citations whose validity depends on the present work. The numerical setup on large systems provides independent, externally verifiable content against known mediated-interaction mechanisms, rendering the central result self-contained rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the numerical model for the bilayer and the assumption that metallic parameters can be tuned without additional effects.

axioms (1)

domain assumption The bilayer geometry preserves the essential 1D character while allowing reservoir effects.
Invoked implicitly when claiming enhancement over the isolated system.

pith-pipeline@v0.9.0 · 5651 in / 1152 out tokens · 42769 ms · 2026-05-19T02:19:11.040902+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Hamiltonian (1) with t_λ, μ_λ, U, t_⊥; fits C_p(i,j) ~ [π A_C / (ξ sinh(π r/ξ))]^{K^{-1}} and S ~ A exp(-r/ξ)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages

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Kivelson, Making high Tc higher: a theoretical pro- posal, Physica B: Condensed Matter 318, 61 (2002)

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work page 2002

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E. Berg, D. Orgad, and S. A. Kivelson, Route to high- temperature superconductivity in composite systems, Phys. Rev. B 78, 094509 (2008)

work page 2008

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Wachtel, A

G. Wachtel, A. Bar-Yaacov, and D. Orgad, Superﬂuid stiﬀness renormalization and critical temperature en- hancement in a composite superconductor, Phys. Rev. B 86, 134531 (2012)

work page 2012

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Zujev, R

A. Zujev, R. T. Scalettar, G. G. Batrouni, and P. Sen- gupta, Pairing correlations in the two-layer attractive Hubbard model, New Journal of Physics 16, 013004 (2014)

work page 2014

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P. M. Dee, S. Johnston, and T. A. Maier, Enhancing T c in a composite superconductor/metal bilayer system: A dynamical cluster approximation study, Physical Review B 105, 214502 (2022)

work page 2022

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Optimizing the critical temperature and superfluid density of a metal-superconductor bilayer

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Huang and J

D. Huang and J. E. Hoﬀman, Monolayer FeSe on SrTiO 3, Annual Review of Condensed Matter Physics 8, 311 (2017)

work page 2017

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A. M. Lobos, A. Iucci, M. M¨ uller, and T. Giamarchi, Dissipation-driven phase transitions in superconducting wires, Phys. Rev. B 80, 214515 (2009)

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F. F. Assaad, M. Bercx, F. Goth, A. G¨ otz, J. S. Hofmann, E. Huﬀman, Z. Liu, F. P. Toldin, J. S. E. Portela, and 6 J. Schwab, Codebase release 2.0 for ALF (Algorithms for Lattice Fermions), SciPost Phys. Codebases , 1 (2022)

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Giamarchi, Quantum Physics in One Dimension (Ox- ford University Press, 2003)

T. Giamarchi, Quantum Physics in One Dimension (Ox- ford University Press, 2003)

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E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer, and P. Werner, Continuous-time Monte Carlo methods for quantum impurity models, Reviews of Mod- ern Physics 83, 349 (2011)

work page 2011

[15] [16]

Bollmark, T

G. Bollmark, T. K¨ ohler, L. Pizzino, Y. Yang, J. S. Hof- mann, H. Shi, S. Zhang, T. Giamarchi, and A. Kan- tian, Solving 2D and 3D Lattice Models of Corre- lated Fermions—Combining Matrix Product States with Mean-Field Theory, Phys. Rev. X 13, 011039 (2023). Supplementary material Strong enhancements to superconducting properties of 1D systems from metal...

work page 2023

[16] [17]

Schollw¨ ock, The density-matrix renormalization group in the age of matrix product states, Ann

U. Schollw¨ ock, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011)

work page 2011

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F. F. Assaad, M. Bercx, F. Goth, A. G¨ otz, J. S. Hofmann, E. Huﬀman, Z. Liu, F. P. Toldin, J. S. E. Portela, and J. Schwab, Codebase release 2.0 for ALF (Algorithms for Lattice Fermions), SciPost Phys. Codebases , 1 (2022)

work page 2022