arxiv: 2510.17452 · v2 · submitted 2025-10-20 · ❄️ cond-mat.supr-con · cond-mat.str-el

Enhanced Superconducting Diode Effect in the Asymmetric Hatsugai-Kohmoto Model

Kai Chen , Pavan Hosur This is my paper

Pith reviewed 2026-05-18 06:14 UTC · model grok-4.3

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

keywords superconducting diode effectHatsugai-Kohmoto interactionstrong electron correlationsasymmetric bandsnonreciprocal supercurrentexactly solvable modelsquality factor

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The pith

Hatsugai-Kohmoto interactions raise the quality factor of the superconducting diode effect in asymmetric metals.

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

The paper examines the superconducting diode effect in systems with strong electron correlations, a regime left mostly unexplored while weak-interaction models dominated earlier studies. It applies the Hatsugai-Kohmoto interaction to asymmetric band metals that already support nonreciprocal supercurrents and shows, via low-energy analysis plus self-consistent numerics, that the interaction improves the diode quality factor. A sympathetic reader would care because the result indicates that strong correlations need not suppress but can instead strengthen the nonreciprocal transport that makes superconducting diodes promising for applications.

Core claim

In asymmetric band metals that host the superconducting diode effect, the Hatsugai-Kohmoto interaction, being local in Bloch momentum space, increases the quality factor of the nonreciprocal supercurrent, as shown by a combination of low-energy analysis and numerical self-consistent calculations.

What carries the argument

The Hatsugai-Kohmoto interaction applied to asymmetric band metals, which remains exactly solvable because of its locality in momentum space and thereby allows controlled study of strong correlations on the superconducting diode effect.

If this is right

Strong electron correlations can improve rather than degrade the performance metric of the superconducting diode effect.
The quality factor of nonreciprocal supercurrent rises once the Hatsugai-Kohmoto interaction is included in the asymmetric band model.
Exactly solvable correlated models become viable platforms for studying and potentially engineering the superconducting diode effect.
Both analytical low-energy methods and numerical self-consistency independently support the reported enhancement.

Where Pith is reading between the lines

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

The same interaction-driven improvement might appear in other momentum-local solvable models once they are coupled to asymmetric bands with superconductivity.
Material searches could target compounds where natural strong correlations already produce larger diode quality factors without external symmetry breaking.
Extensions to finite temperature or weak disorder would test whether the enhanced quality factor survives outside the zero-temperature, clean limit studied here.

Load-bearing premise

The Hatsugai-Kohmoto interaction remains local in Bloch momentum space and keeps the asymmetric band model exactly solvable while preserving the conditions for the superconducting diode effect.

What would settle it

Numerical self-consistent calculations or low-energy analysis that find the superconducting diode quality factor stays the same or decreases after the Hatsugai-Kohmoto interaction is added would falsify the enhancement claim.

Figures

Figures reproduced from arXiv: 2510.17452 by Kai Chen, Pavan Hosur.

**Figure 2.** Figure 2: Superconducting energy spectra E(k) for different Cooper pair momenta q. (a–c) U = 0 and (d–f) U = 2. The spectra E1, E2 and E ′ 1, E ′ 2 are obtained from the Bogoliubovde Gennes (BdG) Hamiltonian with normal-state dispersions ξk and ξk + U, respectively. Gapless points are highlighted by yellow hexagons. The pairing strength is ∆ = 0.5. As shown in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 4.** Figure 4: The Cooper pair momentum asymmetry quantifier [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 3.** Figure 3: Condensation energy Fq and supercurrent Jq as functions of the Cooper pair momentum q. (a, b) Results for the HK interaction strength U = 0. (c, d) Results for U = 4. The temperature T = 0.03. To obtain the superconducting current as a function of q, we first calculate the condensation energy at temperature T, which is expressed as: Fq,∆q = −kBT ˆ d Dk (2π) D ln Zk,q−(∆q = 0 contribution). (6) Here, D deno… view at source ↗

read the original abstract

The superconducting diode effect (SDE), characterized by a nonreciprocal supercurrent, has attracted significant attention in recent years due to its potential applications. However, most studies have focused on weakly correlated models, leaving the impact of strong electron-electron interactions on the SDE largely unexplored. In this work, we bridge this gap by investigating the SDE in asymmetric band metals with Hatsugai-Kohmoto (HK) interaction, which are exactly solvable due to their locality in Bloch momentum space. Through a combination of low-energy analysis and a numerical self-consistent approach, we demonstrate that HK interaction can enhance the SDE's quality factor. Our findings shed light on the role of strong electron-electron correlations in shaping the SDE.

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

HK interactions appear to enhance the SDE quality factor in asymmetric bands, but the self-consistent numerics may quietly relax the exact solvability that makes the model attractive.

read the letter

The main point is that the Hatsugai-Kohmoto interaction raises the quality factor of the superconducting diode effect when the bands are asymmetric. The authors combine a low-energy analytic treatment with numerical self-consistent calculations and report a clear improvement over the non-interacting case. That is the concrete result a reader should take away first. The work is new in applying the solvable HK model specifically to the SDE rather than to equilibrium properties or conventional transport. The choice of an exactly solvable interaction that remains local in momentum space is a reasonable way to bring strong correlations into a transport problem that usually lives in weak-coupling territory. The numerical check on the analytic result is also a positive step; it shows they are not relying solely on perturbation theory. The soft spot sits in the self-consistency loop. The normal-state HK model is solvable because the interaction commutes with the kinetic term at each k. Once a pairing gap is introduced on an asymmetric dispersion, the current response and gap equation couple momenta through the differing velocities. If the numerics require any momentum averaging or decoupling to close the loop, the reported enhancement could partly reflect those choices rather than a pure strong-correlation effect. The abstract presents the result as robust, but the details of how the self-consistency is implemented will decide how much weight the claim can carry. This paper is aimed at people working on superconducting diodes or on solvable models for nonreciprocal transport. A reader already familiar with the HK model and the SDE literature will extract the most value. It is worth sending to a serious referee because the central idea is timely and the approach is technically interesting, even though the numerical implementation needs close examination.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates the superconducting diode effect (SDE) in asymmetric band metals with the Hatsugai-Kohmoto (HK) interaction. The authors state that the momentum-local HK term renders the model exactly solvable, and they combine low-energy analysis with numerical self-consistent calculations to demonstrate that the HK interaction enhances the SDE quality factor relative to the non-interacting case.

Significance. If the central claim is upheld, the work would be significant for extending SDE studies into the strong-correlation regime using a controlled, exactly solvable model. This provides a rare platform to isolate interaction effects on nonreciprocal supercurrent without mean-field approximations, potentially yielding testable predictions for correlated materials and highlighting a mechanism for quality-factor improvement.

major comments (2)

[§4] §4 (Numerical self-consistent calculations): The central claim of enhancement rests on the HK interaction remaining exactly solvable once the asymmetric dispersion and self-consistent pairing gap are introduced. The gap equation couples momenta via the non-reciprocal current response; the manuscript must explicitly show the form of the self-consistency loop and confirm that no momentum averaging or decoupling approximations are required, as any such step could artifactually produce the reported quality-factor increase.
[§3] §3 (Low-energy analysis): The analytic derivation of the enhanced quality factor should be compared quantitatively to the numerical results at the same interaction strengths and asymmetry parameters. Without this direct benchmark, it is unclear whether the low-energy approximation captures the full enhancement or if discrepancies indicate limitations in the analytic treatment.

minor comments (2)

[Figure 3] Figure 3: Axis labels and legends should explicitly state the units of the quality factor and the values of the HK interaction strength U used for each curve.
[Abstract and Introduction] The abstract and introduction could more precisely define the quality factor (e.g., via its explicit formula) to aid readers unfamiliar with SDE literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify the presentation of our results on the superconducting diode effect in the asymmetric Hatsugai-Kohmoto model. We address each major comment below.

read point-by-point responses

Referee: §4 (Numerical self-consistent calculations): The central claim of enhancement rests on the HK interaction remaining exactly solvable once the asymmetric dispersion and self-consistent pairing gap are introduced. The gap equation couples momenta via the non-reciprocal current response; the manuscript must explicitly show the form of the self-consistency loop and confirm that no momentum averaging or decoupling approximations are required, as any such step could artifactually produce the reported quality-factor increase.

Authors: We thank the referee for this important clarification request. The Hatsugai-Kohmoto interaction is strictly local in momentum space, so the full Hamiltonian (including the asymmetric dispersion and the self-consistent pairing term) remains block-diagonal in momentum sectors; each (k, -k) pair is diagonalized exactly and independently. The supercurrent response is computed from the exact eigenstates and eigenvalues of these sectors, and the gap is updated iteratively from the resulting pairing expectation values. No momentum averaging, mean-field decoupling, or inter-momentum approximations enter the loop. In the revised manuscript we will add an explicit description of this self-consistency procedure (including the iterative equations and a schematic of the loop) to make the absence of such approximations fully transparent. revision: yes
Referee: §3 (Low-energy analysis): The analytic derivation of the enhanced quality factor should be compared quantitatively to the numerical results at the same interaction strengths and asymmetry parameters. Without this direct benchmark, it is unclear whether the low-energy approximation captures the full enhancement or if discrepancies indicate limitations in the analytic treatment.

Authors: We agree that a direct quantitative comparison strengthens the manuscript. The current version presents the low-energy analytic expressions and the numerical results separately but does not overlay them at identical parameter values. In the revision we will add a figure (or table) that directly compares the quality factor obtained from the analytic formula with the numerical self-consistent results for several representative values of the HK interaction strength and band asymmetry. This benchmark will allow readers to assess the range of validity of the low-energy approximation and any quantitative discrepancies. revision: yes

Circularity Check

0 steps flagged

No circularity; claims rest on explicit low-energy analysis plus independent numerical self-consistency

full rationale

The paper states that the HK interaction is exactly solvable because it is local in Bloch momentum space, then applies low-energy analysis and a separate numerical self-consistent solution to the gap equation on asymmetric bands. No equation or result is shown to reduce to a fitted input by construction, no load-bearing uniqueness theorem is imported from self-citation, and the enhancement of the quality factor is presented as an output of the explicit calculations rather than a renaming or redefinition of the inputs. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The report rests on the domain assumption that the HK interaction is exactly solvable due to momentum-space locality; no free parameters or invented entities are mentioned in the abstract.

axioms (1)

domain assumption Hatsugai-Kohmoto interaction is local in Bloch momentum space and therefore exactly solvable.
Explicitly invoked in the abstract to justify the model's tractability for studying strong correlations.

pith-pipeline@v0.9.0 · 5652 in / 1060 out tokens · 25735 ms · 2026-05-18T06:14:57.323965+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.lean washburn_uniqueness_aczel unclear

?

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

H(p) = ∑ ξ_p n̂_p,σ + U ∑ n̂_p,↓ n̂_p,↑ with Green’s function (2) and self-consistent Δ_q
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

numerical minimization of F_q,Δq and extraction of η = |J_c^+ − |J_c^−|| / (J_c^+ + |J_c^−|)

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.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Hatsugai-Kohmoto-like Models for Altermagnets and Odd-Parity Magnets
cond-mat.str-el 2026-04 unverdicted novelty 7.0

Generalized Hatsugai-Kohmoto models support ferromagnetism, p- and d-wave bond-ordered magnets, and non-degenerate singlet states with retained spin splitting when local interactions are added.

Reference graph

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