Temperature-Induced Superconductivity Enhancement under Large Exchange Field

arXiv:2511.19030 · cond-mat.supr-con · Submitted 2025-11-24 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Temperature-Induced Superconductivity Enhancement under Large Exchange Field".

Mira: Here's the gist of the paper. The gist The finite temperature can simultaneously weaken superconductivity and mitigate spin polarization induced depairing, leading to potential non-monotonic temperature-dependent behaviors in superconductors subjected to large exchange fields.

Kai: This research demonstrates that superconductivity can be counterintuitively enhanced by temperature when the Zeeman energy exceeds the superconducting order parameter, proposing a multiband effect as a microscopic route for this enhancement.

Mira: Theoretical Framework and Model The study investigates both one-band and two-band superconducting models applicable to arbitrary order parameter symmetries and finite temperatures.

Kai: The Hamiltonian for a two-band system subjected to an external in-plane magnetic field H is given by Equation (1) The free energy F(H, T) is derived in closed form under mean-field and weak-coupling approximations.

Title and authors: Mira: So, we’re talking about this paper's title and who wrote it, and what that actually means for us when we look at the physics of these materials. This work dives into a scenario where temperature does something counterintuitive with superconductivity under a magnetic field. Kai Right, so the focus is on how finite temperature can simultaneously weaken superconductivity and mitigate spin polarization induced depairing. It’s about that competition between thermal effects and magnetic effects that leads to this non-monotonic behavior in superconductors subjected to large exchange fields.

Lev: From an engineering standpoint, what's interesting here is that if we were designing a system, we'd be worried about how this competition plays out at finite temperatures when the Zeeman energy is high. We need to know if the material can handle that thermal mitigation effectively before it starts suppressing the superconductivity itself.

Kai: Exactly. The authors are proposing that in some materials, when the Zeeman energy exceeds the superconducting order parameter, temperature can actually lead to an enhancement of superconductivity compared to zero temperature. They suggest a multiband effect is a microscopic route for this enhancement and they show it using a two-band superconducting model.

Mira: That’s the big picture here—that instead of just getting worse with heat, you can get better in certain conditions because the thermal energy helps manage the magnetic field effects. It sets up a whole new way to think about how temperature interacts with fields in these systems.

The paper's summary: Kai: So, let’s look at what the paper actually summarizes and what it suggests about this enhancement phenomenon. They investigate both one-band and two-band superconducting models with arbitrary order parameter symmetries at finite temperatures. Mira The main finding is that for a one-band s-wave superconductor, increasing temperature generally just suppresses superconductivity monotonically, which means no enhancement by thermal effects there.

Lev: That makes sense for the simple case because the thermal energy just adds to the suppression of the pairing itself when you have a one-band system. We’re looking at how much heat can actually save you from depairing in more complex situations.

Kai: But in two-band systems, they found that temperature-induced superconductivity enhancement appears under specific parameter conditions, defined by x. This means it doesn't happen everywhere; it’s conditional on the material setup.

Mira: The enhancement itself is characterized by two key features: first, a temperature-induced nonmonotonic behavior of the order parameter, and second, an enhancement of hc when you look at the critical field. That hc enhancement is tied to how we tune those system parameters alpha and gamma.

Lev: So they’re saying this effect isn't just some random quirk; it depends heavily on the ratio between the order parameters alpha and the density of states ratios gamma. That tells us where we actually need to look for these effects in materials.

The paper's improvements: Kai: Now, let’s talk about what improvements this paper suggests to the existing understanding of temperature-induced superconductivity enhancement. They show that the properties of two-band systems depend strongly on those ratios alpha and gamma. Mira Specifically, for two-band systems with large alpha and small gamma, superconductivity is dominated by the larger order parameter, which they say resembles a one-band system characterized by a smaller order parameter.

Lev: That’s interesting because it means in those regimes, you might be able to get some enhancement even if you're not in the "ideal" two-band configuration for it. It suggests robustness across different structural parameters.

Kai: The enhancement of hc specifically appears only within an appropriate region of the parameter space where alpha and gamma are roughly comparable, which is a very specific constraint on the material’s properties. Mira This means we can predict *where* to look in terms of how alpha and gamma are tuned to find that hc enhancement.

Lev: And they also showed this phenomenon extends beyond s-wave pairing symmetries, applying it to many other pairings, like d-wave symmetry in one-band superconductors. That broadens the scope of where we can expect this temperature effect to show up.

Conclusion: Kai: So to wrap up on this paper, the enhancement is characterized by that nonmonotonic order parameter behavior and that hc enhancement we talked about earlier. Mira They found that this enhancement is really sensitive to alpha and gamma, specifically only systems with large gamma and intermediate alpha exhibit a clear hc enhancement.

Lev: And they also showed how the superconducting order parameter x(t) changes with the applied field h. When h gets large enough to induce a first-order transition at finite temperature rather than zero, you see an abrupt drop, then a gradual recovery, and then suppression when the temperature goes up further.

Kai: It really shows that the behavior of the superconducting order parameter isn't just monotonic with temperature under a magnetic field in these complex systems. Mira The paper ends by pointing to two-band s-wave systems like MgB two and NbSe two and anisotropic superconductors like CeCoIn five and FeSe, as ideal platforms for testing these predictions.

Lev: We're looking at how the competition between thermal energy and magnetic effects can lead to this complex behavior in superconductors under large exchange fields. That’s what this paper on "Temperature-Induced Superconductivity Enhancement under Large Exchange Field" is all about.

State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University · Frontier Science Center for Quantum Information

cond-mat.supr-con

Submitted: 2025-11-24

Updated: 2025-11-24

Comments: 5 pages and 4 figures for main text; 13 pages and 11 figures for Supplementary Material

Journal ref: Phys. Rev. Research 8, 043079 (2026)

DOI: 10.1103/6q41-1cxp

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 72/100

The gist: The gist The finite temperature can simultaneously weaken superconductivity and mitigate spin polarization induced depairing, leading to potential non-monotonic temperature-dependent behaviors in

Key concepts

Spin Polarization Induced Depairing: When a strong magnetic field aligns electron spins (spin polarization), it can break Cooper pairs in superconductors, weakening the superconducting state. This depairing effect is usually detrimental to superconductivity.
Two-Band System: This model describes superconductors with two distinct types of electrons or superconducting order parameters, represented by $\Delta_1$ and $\Delta_2$. The interaction between these two bands is crucial for understanding the complex temperature and field responses described in the research.
Order Parameter Ratios ($\alpha$ and $\gamma$): These parameters define the relative strengths of the different superconducting order parameters ($\alpha$) and the densities of states ($\\gamma$). The behavior of these ratios determines whether a system shows enhancement, suppression, or a specific phase transition type.
Two-Band Featured Regime: This is an intermediate parameter region for two-band systems where the interplay between $\Delta_1$ and $\Delta_2$ leads to complex behavior. This regime is characterized by exhibiting two distinct first-order transitions under magnetic fields.

Terminology

Polarization — 1× in this paper · explained in 2 episodes

Summary

The gist The finite temperature can simultaneously weaken superconductivity and mitigate spin polarization induced depairing, leading to potential non-monotonic temperature-dependent behaviors in superconductors subjected to large exchange fields. This research demonstrates that superconductivity can be counterintuitively enhanced by temperature when the Zeeman energy exceeds the superconducting order parameter, proposing a multiband effect as a microscopic route for this enhancement.

Theoretical Framework and Model

The study investigates both one-band and two-band superconducting models applicable to arbitrary order parameter symmetries and finite temperatures. The Hamiltonian for a two-band system subjected to an external in-plane magnetic field H is given by Equation (1) The free energy F(H, T) is derived in closed form under mean-field and weak-coupling approximations. The dimensionless free energy is expressed in Eq. (S12) The analysis proceeds by minimizing this free energy to find the self-consistent order parameters.

One-Band Superconductor Analysis

For a one-band s-wave superconductor, increasing temperature generally suppresses superconductivity monotonically <ref:2511.19030 pg3, In contrast, for the one-band case, the h-t phase diagram in Fig. 2(a) shows that the critical field hc reaches its maximum at zero temperature and gradually decreases with increasing temperature <ref:2511.19030 pg3, The contour lines of the order parameter extend monotonically from the upper-left to the lower-right corner, indicating that superconductivity is not enhanced by thermal effects <ref:2511.19030#pg4>.

Two-Band Superconductor Enhancement

Temperature-induced superconductivity enhancement appears in two-band systems under specific parameter conditions x, allowing thermal effects to more effectively mitigate the depairing caused by the exchange field <ref:2511.19030#pg5>.

Dependence on Parameters and Symmetries

The enhancement of superconductivity is characterized by two key features: the temperature-induced nonmonotonic behavior of the order parameter and hc enhancement <ref:2511.19030 pg5, The properties of two-band systems depend strongly on the ratio of order parameters α and the ratio of densities of states γ, as defined in Eq. (3) <ref:2511.19030 pg8, For two-band systems with large α and small γ, superconductivity is dominated by the larger order parameter ∆2, resembling a one-band system characterized by ∆2 <ref:2511.19030#pg5>. The enhancement of hc appears only within an appropriate region of the parameter space, where α and γ are roughly comparable.

Anisotropic Pairing Symmetries

The phenomenon of temperature-induced superconductivity enhancement can be extended to many other pairing symmetries beyond s-wave <ref:2511.19030 pg7, In anisotropic one-band superconductors, such as d-wave symmetry (χ(ϕ) = cos 2ϕ), the system is more promising to exhibit temperature-induced enhancement than isotropic one-band system <ref:2511.19030#pg8>.

Phase Transition Order

Two-band superconductors exhibit three distinct types of behavior depending on the parameters α and γ <ref:2511.19030 pg8, The first type is ∆1-dominated, occurring in the region of small α and relatively large γ, exhibiting a single FOT <ref:2511.19030#pg9>. The second type is ∆2-dominated, found at large α and relatively small γ, where an insignificant SOT appears at a low field (h ≈ x) due to the influence of ∆1, followed by a FOT at the critical field <ref:2511.19030#pg9>. The third type, referred to as the two-band featured regime, emerges at intermediate α and γ and exhibits two FOTs <ref:2511.19030#pg9>.

Experimental Relevance

The theoretical predictions can be directly tested by transport and tunneling measurements on multiband superconducting thin films under large in-plane magnetic field <ref:2511.19030 pg5, Two-band s-wave systems such as MgB2 [33–36] and NbSe2 [37–40], as well as anisotropic (possibly dwave) two-band superconductors including CeCoIn5 [41–44] and FeSe [45–48], provide ideal platforms for such verification <ref:2511.19030#pg6>. In MgB2, tunneling measurements [36] reveal spatial variations in the ratio of densities of states γ, offering a natural setting to test our s-wave predictions <ref:2511.19030#pg8>. Moreover, previous studies have shown that both the densities of states ratio γ and the order parameter ratio α can be tuned by substrate-induced hole doping [49, 50], making FeSe a particularly promising candidate for experimentally validating our theoretical framework <ref:2511.19030#pg8>.

Conclusion on Enhancement Signatures

The enhancement of superconductivity is characterized by two key features: the temperature-induced nonmonotonic behavior of the order parameter and hc enhancement <ref:2511.19030 pg5, We found that this enhancement is highly sensitive to the parameters α and γ: only systems with large γ and intermediate α exhibit clear hc enhancement, whereas non-monotonic order-parameter behavior can arise whenever α and γ are not small <ref:2511.19030#pg6>. Our theoretical predictions, the temperature-induced hc enhancement and the non-monotonic temperature dependence of the order parameter, can be directly tested by transport and tunneling measurements on multiband superconducting thin films under large in-plane magnetic field <ref:2511.19030#pg6>. The two-band s-wave systems such as MgB2 [33–36] and NbSe2 [37–40], as well as anisotropic (possibly dwave) two-band superconductors including CeCoIn5 [41–44] and FeSe [45–48], provide ideal platforms for such verification <ref:2511.19030#pg8>. The behavior of the superconducting order parameter x(t) varies with the applied field h <ref:2511.19030 pg6, When h becomes large enough to induce a FOT at finite temperature rather than at zero, the order parameter exhibits a sequence of behaviors: an abrupt drop, a gradual recovery, and then suppression with further temperature <ref:2511.19030#pg7>.

Improvements for AI systems

System capable of predicting non-monotonic temperature-dependent superconducting behavior under large exchange fields by analyzing free energy competition between thermal suppression and spin polarization depairing, as demonstrated by the competition between thermal and magnetic effects leading to a non-monotonic temperature-dependent behaviors in superconductors subjected to large exchange fields.
AI system can perform quantitative parameter mapping of superconductivity enhancement by correlating the ratio parameters α and γ with the occurrence of hc enhancement, specifically identifying that this phenomenon is highly sensitive to the parameters α and γ: only systems with large γ and intermediate α exhibit clear hc enhancement.
The system can simulate phase transition order in two-band superconductors based on parameter regimes, distinguishing between three types of behavior: the first type is ∆1-dominated, occurring in the region of small α and relatively large γ, the second type is ∆2-dominated, found at large α and relatively small γ, and the third type, referred to as the two-band featured regime.
The AI can predict the specific order of phase transitions (e.g., two FOTs in the two-band featured regime) by analyzing field dependence of order parameter profiles, identifying a discontinuity in x(h) accompanied by a divergent peak in dx/dh for a first-order transition.
The system can model and predict specific non-monotonic behaviors like double-extrema structure in hc(t) or a distinct non-monotonic behavior in the low-field region near h ≈ x by analyzing temperature evolution maps of the order parameter, as seen in hc first decreases, then increases, and finally decreases again with rising temperature.