超导性

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新提交 (展示 2 之 2 条目 )

[1] arXiv:2508.03364 [中文pdf, pdf, html, 其他]

标题： 通过反铁磁性在超导体中工程化亚能隙态 显示英文标题

标题： Engineering subgap states in superconductors by altermagnetism

Bo Lu, Phillip Mercebach, Pablo Burset, Keiji Yada, Jorge Cayao, Yukio Tanaka, Yuri Fukaya

主题： 超导性 (cond-mat.supr-con) ; 中尺度与纳米尺度物理 (cond-mat.mes-hall)

我们研究通过定制的反磁场在非常规超导体上实现和控制亚能隙态。 当反磁性的对称性和非常规超导性的对称性对齐时，我们展示了体零能平带的出现，从而产生零偏压电导峰。 $d$和$g$波反磁体的对称性和强度强烈影响来自$d$波和手征$d$和$p$波超导体的表面安德列夫态。 因此，实现了不同类型的亚能隙态，包括弯曲和平带，可以通过隧穿谱学进行检测。 此外，我们发现由反磁性引起的亚能隙态在净磁化为零时会产生大的自旋电导率，这有助于识别底层反磁性和超导性的强度。 我们的结果为设计和操控超导系统中的亚能隙态提供了一条坚实的道路，这可能对功能化超导自旋电子器件有用。 显示英文摘要

We investigate the realization and control of subgap states by tailored altermagnetic fields on unconventional superconductors. When the symmetries of altermagnetism and unconventional superconductivity align, we demonstrate the emergence of bulk zero-energy flat bands, giving rise to a zero-bias conductance peak. The symmetry and strength of $d$- and $g$-wave altermagnets strongly affect the surface Andreev states from $d$-wave and chiral $d$- and $p$-wave superconductors. As a result, distinct types of subgap states are realized, including curved and flat bands, that can be detected by tunneling spectroscopy. Furthermore, we find that the altermagnetism-induced subgap states give rise to a large spin conductance at zero net magnetization which helps identify the strength of the underlying altermagnetism and superconductivity. Our results offer a solid route for designing and manipulating subgap states in superconducting systems, which can be useful for functionalizing superconducting spintronic devices.

[2] arXiv:2508.03414 [中文pdf, pdf, 其他]

标题： 间隙氧有序性及其与超导性的竞争在La$_2$PrNi$_2$O$_{7+δ}$中 显示英文标题

标题： Interstitial oxygen order and its competition with superconductivity in La$_2$PrNi$_2$O$_{7+δ}$

Zehao Dong, Gang Wang, Ningning Wang, Wen-Han Dong, Lin Gu, Yong Xu, Jinguang Cheng, Zhen Chen, Yayu Wang

评论： 将出现在《自然材料》（2025）中

主题： 超导性 (cond-mat.supr-con) ; 材料科学 (cond-mat.mtrl-sci) ; 强关联电子 (cond-mat.str-el)

高温压力下双层镍氧化物La$_3$Ni$_2$O$_7$的超导性在凝聚态物理中引起了广泛关注。 虽然早期样品表现出有限的超导体积分数，但用Pr替代La使得多晶在压力下实现了体超导性，并在常压下提高了薄膜的转变温度。 除了稀土掺杂外，适度的氧或臭氧退火通过缓解氧空位来改善超导性，而高压氧退火则在所有压力范围内导致平凡的非超导金属态。 这些发现突显了阐明Pr掺杂和氧化学计量学在调节双层镍氧化物超导性中的单独和综合效应的必要性。 在这里，利用多层电子ptychography和电子能量损失谱学，我们研究了生长的La$_2$PrNi$_2$O$_7$和高压氧退火的La$_2$PrNi$_2$O$_{7+\delta}$多晶的结构和电子性质。 我们发现Pr掺杂剂优先占据外层La位点，有效消除内层顶氧空位，并确保在压力下具有体超导性的生长态La$_2$PrNi$_2$O$_7$接近化学计量比。 相比之下，高压氧退火诱导出条纹状间隙氧排列，将准一维晶格势和过量空穴载流子引入p-d杂化轨道，最终抑制超导性。 这种行为与铜基超导体形成鲜明对比，因为在铜基超导体中，类似的间隙氧排列会增强超导性。 我们的研究结果揭示了条纹状间隙氧排列与双层镍氧化物中超导性的竞争关系，为理解其不同的配对机制提供了关键见解，并为设计更稳定的超导相提供了路线图。 显示英文摘要

High-temperature superconductivity in bilayer nickelate La$_3$Ni$_2$O$_7$ under pressure has attracted significant interest in condensed matter physics. While early samples exhibited limited superconducting volume fractions, Pr substitution for La enabled bulk superconductivity in polycrystals under pressure and enhanced transition temperatures in thin films at ambient pressure. Beyond rare-earth doping, moderate oxygen or ozone annealing improves superconductivity by mitigating oxygen vacancies, whereas high-pressure oxygen annealing leads to a trivial, non-superconducting metallic state across all pressure regimes. These findings highlight the need to elucidate both the individual and combined effects of Pr doping and oxygen stoichiometry in modulating superconductivity in bilayer nickelates. Here, using multislice electron ptychography and electron energy-loss spectroscopy, we investigate the structural and electronic properties of as-grown La$_2$PrNi$_2$O$_7$ and high-pressure-oxygen-annealed La$_2$PrNi$_2$O$_{7+\delta}$ polycrystals. We find that Pr dopants preferentially occupy outer La sites, effectively eliminating inner-apical oxygen vacancies and ensuring near-stoichiometry in as-grown La$_2$PrNi$_2$O$_7$ that is bulk-superconducting under pressure. In contrast, high-pressure oxygen annealing induces a striped interstitial oxygen order, introducing quasi-1D lattice potentials and excess hole carriers into p-d hybridized orbitals, ultimately suppressing superconductivity. This behavior starkly contrasts with cuprate superconductors, where similar interstitial oxygen ordering enhances superconductivity instead. Our findings reveal a competition between striped interstitial oxygen order and superconductivity in bilayer nickelates, offering key insights into their distinct pairing mechanisms and providing a roadmap for designing more robust superconducting phases.

交叉提交 (展示 3 之 3 条目 )

[3] arXiv:2508.03219 (交叉列表自 cond-mat.mes-hall) [中文pdf, pdf, html, 其他]

标题： 量子双极热电性 显示英文标题

标题： Quantum Bipolar Thermoelectricity

Filippo Antola, Giorgio De Simoni, Francesco Giazotto, Alessandro Braggio

主题： 中尺度与纳米尺度物理 (cond-mat.mes-hall) ; 超导性 (cond-mat.supr-con) ; 量子物理 (quant-ph)

热电效应通常起源于与能量相关的输运不对称性。 在本文中，我们探讨了一种纯粹的量子热电效应，该效应源于低温量子浴的发射/吸收不对称性。 我们提出了一种间隙不对称的S-I-S'超导隧道结，在热平衡状态下，与低温电磁环境耦合，由于动态库仑阻塞而产生非线性量子双极热电效应。 分析了实际实现的关键性能特征。 显示英文摘要

Thermoelectricity usually originates from energy-dependent transport asymmetries. In this Letter, we explore a purely quantum thermoelectric effect rooted in the emission/absorption asymmetry of a low-temperature quantum bath. We propose a gap-asymmetric S-I-S' superconducting tunnel junction in thermal equilibrium, coupled to a low-temperature electromagnetic environment, which develops a nonlinear quantum bipolar thermoelectric effect due to the dynamical Coulomb blockade. Key performance features are analyzed for realistic implementations.

[4] arXiv:2508.03427 (交叉列表自 cond-mat.mtrl-sci) [中文pdf, pdf, html, 其他]

标题： 由对称性破缺引起的FeSe拓扑结构 显示英文标题

标题： Symmetry-breaking-induced topology in FeSe

Mikel García-Díez, Jonas B. Profe, Augustin Davignon, Steffen Backes, Roser Valentí, Maia G. Vergniory

评论： 9页，5图

主题： 材料科学 (cond-mat.mtrl-sci) ; 强关联电子 (cond-mat.str-el) ; 超导性 (cond-mat.supr-con)

FeSe在过去二十年中一直是研究最深入的铁基超导体之一，表现出多种现象，如非常规超导性、向列序、磁性、轨道选择性关联和结构相变。 虽然在某些情况下已经识别出拓扑非平凡相——例如碲掺杂的FeSe和单层FeSe——但体相FeSe中的拓扑性质大多尚未被探索。 在这项工作中，我们提出了一种在体相FeSe中直接实现拓扑相的新途径。 我们证明，破坏面内$C_4$旋转对称性，从而降低晶体对称性，可以将FeSe带入强拓扑绝缘相。 为了支持这一点，我们进行了密度泛函理论计算，并使用拓扑量子化学和基于对称性的指标分析能带结构。 我们的结果表明，单轴应变和向正交低温相的结构转变都会导致非平凡的能带拓扑。 此外，通过动力学平均场理论引入电子关联表明，费米能级附近的拓扑特性保持稳健，因为相关能带仅经历适度的重整化。 这些发现突显了应变作为在FeSe中诱导拓扑相的一种有前景的机制。 显示英文摘要

FeSe has been one of the most intensively studied iron-based superconductors over the past two decades, exhibiting a wide range of phenomena such as unconventional superconductivity, nematic order, magnetism, orbital-selective correlations, and structural phase transitions. While topologically non-trivial phases have been identified in certain cases - such as Te-doped FeSe and monolayer FeSe - topology in bulk FeSe has largely remained unexplored. In this work, we propose a new route to realize topological phases directly in bulk FeSe. We demonstrate that breaking the in-plane $C_4$ rotational symmetry, thereby lowering the crystal symmetry, can drive FeSe into a strong topological insulating phase. To support this, we perform density functional theory calculations and analyze the band structure using topological quantum chemistry and symmetry-based indicators. Our results show that both uniaxial strain and the structural transition to the orthorhombic low-temperature phase lead to non-trivial band topology. Moreover, incorporating electronic correlations through dynamical mean field theory reveals that the topological characteristics near the Fermi level remain robust, as the relevant bands experience only moderate renormalization. These findings highlight strain as a promising mechanism to induce topological phases in FeSe.

[5] arXiv:2508.03528 (交叉列表自 cond-mat.mes-hall) [中文pdf, pdf, html, 其他]

标题： 非平衡非线性热电模型在超导隧道结中的应用 显示英文标题

标题： Out-of-equilibrium nonlinear model of thermoelectricity in superconducting tunnel junctions

Leonardo Lucchesi, Federico Paolucci

评论： 10页，6图

主题： 中尺度与纳米尺度物理 (cond-mat.mes-hall) ; 超导性 (cond-mat.supr-con)

热电效应在超导隧道结中的研究一直是在冷侧与热浴之间处于平衡的假设下进行的，通常在线性范围内。 我们定义了一个更完整的非平衡非线性数值模型，在低功率极限下该模型会退化为平衡线性模型。 我们发现，对于实际实验装置中合理的参数，线性模型不能正确描述超导隧道结的行为。 随后，我们展示了模型之间的定性和定量差异，发现对于高功率，结会饱和并随后反转其行为。 最后，我们还澄清了线性和非线性热电效应之间的差异，并设计了一个新的准则来在参数空间中找到非线性热电效应。 显示英文摘要

Thermoelectricity in superconducting tunnel junctions has always been studied under the hypothesis of equilibrium between the cold side and the thermal bath, usually in the linear regime. We define a more complete out-of-equilibrium nonlinear numerical model that reduces to the equilibrium linear model in the low-power limit. We find that the linear model does not correctly describe the behavior of superconducting tunnel junctions for parameters that are reasonable in practical experimental setups. Subsequently, we present the qualitative and quantitative differences between the models, discovering that for high power, the junction saturates and then inverts its behavior. Finally, we also clarify the difference between linear and nonlinear thermoelectricity and devise a new criterion to find nonlinear thermoelectricity in the parameter space.

替换提交 (展示 6 之 6 条目 )

[6] arXiv:2409.16114 (替换) [中文pdf, pdf, html, 其他]

标题： 拓扑手性超导性通过扭曲双层WSe$_2$中的谷间反铁磁涨落介导 显示英文标题

标题： Topological Chiral Superconductivity Mediated by Intervalley Antiferromagnetic Fluctuations in Twisted Bilayer WSe$_2$

Wei Qin, Wen-Xuan Qiu, Fengcheng Wu

评论： 7+14页，5+11图

主题： 超导性 (cond-mat.supr-con) ; 中尺度与纳米尺度物理 (cond-mat.mes-hall)

Motivated by the recent observations of superconductivity in twisted bilayer WSe$_2$ (tWSe$_2$), we theoretically investigate the superconductivity driven by electronic mechanism. We first demonstrate that the multi-band screened Coulomb interaction within the random phase approximation is insufficient to induce observable pairing instability. Nevertheless, by further including the intervalley antiferromagnetic fluctuations, the pairing interaction is substantially enhanced, yielding superconductivity with critical temperature $T_c$ of hundreds of millikelvin at van Hove singularities. The predicted $T_c$ increases with increasing the displacement field and corresponds to a doubly-degenerate $d$-wave-like pairing, which evolves into topological chiral $d \pm id$ superconductor below $T_c$. 超导性和谷反铁磁性之间的相互作用导致了与实验观察一致的相图。这些发现确立了谷涨落作为tWSe$_2$中的主要配对胶水。 显示英文摘要

Motivated by the recent observations of superconductivity in twisted bilayer WSe$_2$ (tWSe$_2$), we theoretically investigate the superconductivity driven by electronic mechanism. We first demonstrate that the multi-band screened Coulomb interaction within the random phase approximation is insufficient to induce observable pairing instability. Nevertheless, by further including the intervalley antiferromagnetic fluctuations, the pairing interaction is substantially enhanced, yielding superconductivity with critical temperature $T_c$ of hundreds of millikelvin at van Hove singularities. The predicted $T_c$ increases with increasing the displacement field and corresponds to a doubly-degenerate $d$-wave-like pairing, which evolves into topological chiral $d \pm id$ superconductor below $T_c$. The interplay between superconductivity and intervalley antiferromagnetism results in a phase diagram consistent with experimental observations.These findings establish intervalley fluctuations as the primary pairing glue in tWSe$_2$.

[7] arXiv:2410.07337 (替换) [中文pdf, pdf, html, 其他]

标题： 电压可调的自旋超电流非互易性达到100%效率 显示英文标题

标题： Voltage-tunable spin supercurrent nonreciprocity reaching 100% efficiency

Chi Sun, Johanne Bratland Tjernshaugen, Jacob Linder

评论： 10页，12图

期刊参考： 物理评论B 112, 064504 (2025)

主题： 超导性 (cond-mat.supr-con)

超导二极管效应的版本在过去几年中一直是广泛研究的主题。到目前为止，研究几乎全部集中在电荷输运上，但一个自然的问题是，是否可以在没有耗散的情况下获得非互易自旋输运。在这里，我们证明可以使用超导/铁磁多层结构产生可电调制的由超电流携带的非互易自旋输运。非互易自旋超电流达到理想的效率100%，这意味着临界电流的自旋极化在一个流动方向上是有限的，而在另一个方向上则消失。我们解释了产生这种现象的基本物理原理。这一结果提供了一种将具有自旋极化的非互易超电流集成的方法，为基于约瑟夫森结的量子技术提供了新的功能。 显示英文摘要

The superconducting version of a diode effect has been the subject of extensive research in the past few years. So far, the focus has almost exclusively been on charge transport, but a natural question is whether it is possible to obtain nonreciprocal spin transport without dissipation. Here, we demonstrate that it is possible to generate electrically tunable nonreciprocal spin transport carried by a supercurrent using superconductor/ferromagnet multilayers. The nonreciprocal spin supercurrent reaches an ideal efficiency of 100%, meaning that the spin-polarization of the critical current is finite in one flow direction whereas it vanishes in the other direction. We explain the underlying physics generating this phenomenon. This result provides a way to integrate nonreciprocal supercurrents with spin-polarization, offering new functionality in quantum technologies based on Josephson junctions.

[8] arXiv:2501.05451 (替换) [中文pdf, pdf, html, 其他]

标题： 非常规超导平台上演奏的反铁磁性与拓扑超导性的相互作用 显示英文标题

标题： Interplay between altermagnetism and topological superconductivity on an unconventional superconducting platform

Pritam Chatterjee, Vladimir Juričić

评论： 11页，6图，已发表版本

期刊参考： 物理评论B 112, 054503 (2025)

主题： 超导性 (cond-mat.supr-con) ; 中尺度与纳米尺度物理 (cond-mat.mes-hall)

我们提出一个理论模型来研究反铁磁性与$p$波超导性的相互作用，特别关注二维（2D）$p$波超导体中的拓扑相变，考虑手性和螺旋相。 我们的研究表明，螺旋和手性马约拉纳态的出现可以通过$d-$波反铁磁序参数的振幅进行调节，结果取决于超导态的性质。 在螺旋超导体中，这种反铁磁体可以诱导进入一种无能隙的拓扑超导体，该超导体包含马约拉纳平带边缘模式。 另一方面，在手性超导体中，拓扑转变发生在非平凡的有能隙拓扑相和无能隙节点线超导体之间，其中 Bogoliubov 准粒子能带在动量空间中的一条孤立线上相交。 值得注意的是，我们表明当这种反铁磁体与同时具有手性和螺旋成分的混合配对超导体耦合时，会形成一种混合拓扑相，其特征是色散的马约拉纳边缘模式与几乎平带的马约拉纳边缘态共存。 因此，我们的发现建立了一个新的平台，用于控制和操控总磁化为零的非常规超导体中的马约拉纳模。 显示英文摘要

We propose a theoretical model to investigate the interplay between altermagnetism and $p$-wave superconductivity, with a particular focus on topological phase transitions in a two-dimensional (2D) $p$-wave superconductor, considering both chiral and helical phases. Our study reveals that the emergence of helical and chiral Majorana states can be tuned by the amplitude of a $d-$wave altermagnetic order parameter, with the outcome depending on the nature of the superconducting state. In the helical superconductor, such an altermagnet can induce a topological phase transition into a gapless topological superconductor hosting Majorana flat edge modes. On the other hand, in the chiral superconductor, the topological transition takes place between a topologically nontrivial gapped phase and a gapless nodal-line superconductor, where the Bogoliubov quasiparticle bands intersect at an isolated line in momentum space. Remarkably, we show that when such an altermagnet is coupled to a mixed-pairing superconductor, with both chiral and helical components, a hybrid topological phase emerges, featuring dispersive Majorana edge modes that coexist with nearly flat Majorana edge states. Our findings therefore establish a novel platform for controlling and manipulating Majorana modes in unconventional superconductors with vanishing total magnetization.

[9] arXiv:2508.00460 (替换) [中文pdf, pdf, html, 其他]

标题： 拓扑超导体/铁磁绝缘体薄膜异质结构中的混合磁子-纳姆布-戈德斯通激发 显示英文标题

标题： Hybrid magnon -- Nambu-Goldstone excitations in topological superconductor/ferromagnetic insulator thin-film heterostructures

T. Karabassov, I. V. Bobkova, A. M. Bobkov, A. S. Vasenko, A. A. Golubov

主题： 超导性 (cond-mat.supr-con) ; 中尺度与纳米尺度物理 (cond-mat.mes-hall)

我们研究了一种之前未被探索的动态邻近效应，该效应发生在s波拓扑超导体/铁磁绝缘体（TS/FI）异质结构中。 预测在FI中的磁振子和TS中的Nambu-Goldstone（NG）集体超导相模之间会发生耦合，形成复合磁振子-NG激发态。 这种耦合的机制与TS螺旋表面态中电子的完全自旋-动量锁定有关。 磁振子-NG耦合的强度相对于磁振子波矢和FI平衡磁化方向的相互取向表现出强烈的各向异性。 这种效应提供了一种将自旋信号与由集体超导激发携带的无自旋信号相互转换的机制，从而为超导自旋电子学的发展提供了新的动力。 显示英文摘要

We address a previously unexplored type of dynamical proximity effect that occurs in s-wave topological superconductor/ferromagnetic insulator (TS/FI) heterostructures. It is predicted that magnons in the FI and the Nambu-Goldstone (NG) collective superconducting phase mode in the TS are coupled, forming composite magnon-NG excitations. The mechanism of this coupling is associated with the complete spin-momentum locking of electrons in the helical surface state of the TS. The strength of the magnon-NG coupling is strongly anisotropic with respect to the mutual orientation of the magnon wave vector and the equilibrium magnetization of the FI. This effect provides a mechanism for the interconversion of spin signals and the spinless signals carried by collective superconducting excitations, thereby giving new impetus to the development of superconducting spintronics.

[10] arXiv:2508.00499 (替换) [中文pdf, pdf, html, 其他]

标题： 拓扑超导体/铁磁绝缘体异质结构中的混合集体激发理论 显示英文标题

标题： Theory of hybrid collective excitations in topological superconductor/ferromagnetic insulator heterostructures

T. Karabassov, I. V. Bobkova, A. M. Bobkov, A. S. Vasenko, A. A. Golubov

主题： 超导性 (cond-mat.supr-con) ; 中尺度与纳米尺度物理 (cond-mat.mes-hall)

我们为拓扑超导体/铁磁绝缘体（TS/FI）混合结构中的动态邻近效应发展了一种线性响应理论。 我们的方法结合了TS中电子格林函数的非平衡准经典Keldysh-Usadel方程和控制FI中磁化动力学的Landau-Lifshitz-Gilbert方程。 在这一框架下，我们研究了由邻近效应引起的自旋波与超导集体激发之间的耦合。 我们发现TS表面态固有的自旋-动量锁定导致超导Nambu-Goldstone（相位）集体模与自旋波之间的杂化，从而产生复合自旋波-Nambu-Goldstone激发。 耦合强度对相关物理参数的依赖关系通过分析和数值方法进行了分析。 相反，我们表明Higgs（振幅）模在一级近似下不与自旋波耦合，因此不参与杂化集体激发的形成。 显示英文摘要

We develop a linear response theory for the dynamical proximity effect in topological superconductor/ferromagnetic insulator (TS/FI) hybrid structures. Our approach combines the nonequilibrium quasiclassical Keldysh-Usadel equations for the electronic Green's functions in the TS with the Landau-Lifshitz-Gilbert equation governing the magnetization dynamics in the FI. Within this framework, we study the proximity-induced coupling between magnons and superconducting collective excitations. We find that the spin-momentum locking intrinsic to the surface state of the TS leads to a hybridization between the superconducting Nambu-Goldstone (phase) collective mode and magnons, resulting in the emergence of composite magnon-Nambu-Goldstone excitations. The dependence of the coupling strength on relevant physical parameters is analyzed both analytically and numerically. In contrast, we show that the Higgs (amplitude) mode does not couple to magnons at linear order and therefore does not participate in the formation of hybrid collective excitations.

[11] arXiv:2405.08874 (替换) [中文pdf, pdf, html, 其他]

标题： 一种来自标准模型动力学的暗物质费米子量子流体 显示英文标题

标题： A Dark Matter Fermionic Quantum Fluid from Standard Model Dynamics

Stephon Alexander, Heliudson Bernardo, Humberto Gilmer

评论： 12页，4页的附录

主题： 高能物理 - 现象学 (hep-ph) ; 宇宙学与非星系天体物理学 (astro-ph.CO) ; 超导性 (cond-mat.supr-con) ; 广义相对论与量子宇宙学 (gr-qc)

我们提出一种暗物质模型，即右手中微子或类矢量夸克的库珀对的超导流体。 超导暗物质分别由标准模型希格斯和色规范作用中的吸引通道引起。 我们表明，对于每种情况，间隙方程的解在适当的化学势值下提供了可行的暗物质候选者。 该机制产生一种超轻中微子凝聚态，其质量为$m_{\rm DM} \sim 10^{-19} \text{eV}$，或者是一种具有广泛可能质量范围的类矢量夸克凝聚态。 该模型的宇宙学和粒子物理约束导致有效相对论物种数量$N_{\rm eff}$与费米子生成时的化学势和CMB温度之间的联系。 我们还发现超导费米子密度与重子密度之间的关系，这对标准宇宙学中暗物质与重子密度之间的巧合有影响。 鉴于中微子的自然$\text{eV}$尺度，这种机制可能对哈勃张力有影响。 显示英文摘要

We present a model of dark matter as a superconducting fluid of Cooper pairs of right handed neutrinos or of vector-like quarks. The superconducting dark matter is induced by attractive channels in the Standard Model Higgs and color sectors of the Standard Model, respectively. We show that, for each case, the solution to the gap equation provides viable dark matter candidates for suitable chemical potential values. The mechanism yields an ultra-light neutrino condensate with a mass of $m_{\rm DM} \sim 10^{-19} \text{eV}$ or a vector-like quark condensate with wide range of possible masses. Both cosmological and particle physics constraints on the model lead to a connection between the number of effective relativistic species $N_{\rm eff}$, and the chemical potential and CMB temperature at the time of fermion creation. We also find a relation between the superconducting fermion and baryon densities, with implications for the coincidence between the dark matter and baryon densities in standard cosmology. Given the natural $\text{eV}$ scale of neutrinos, this mechanism may have implications for the Hubble tension.