Ekaterina Vlasiuk of Heidelberg University, Manfred Salmhofer of Heidelberg University, Eugene Demler of ETH Zürich and Richard Schmidt of Heidelberg University report a way to robustly increase the critical temperature of superconductors by coupling them to thermal bosons. Their work uses a renormalization group approach to describe how boson-induced attraction between fermions competes with density fluctuations, predicting a critical temperature increase across a wide range of interactions.

The researchers established a phase diagram differentiating enhanced superconductivity based on whether the bosons are condensed or in a thermal state, outlining potential realizations in cold atomic systems and van der Waals heterostructures. They explore whether coupling to a thermal bosonic medium can change established bounds on the critical temperature.

Boson-Driven Enhancement of Superconducting Critical Temperature

A theoretical framework predicts a superconductor’s critical temperature can more than double when coupled with a thermal boson bath, potentially opening avenues for higher-temperature superconducting materials. Calculations reveal this enhancement is robust across a range of interactions, though it diminishes as the superconductor itself approaches its inherent temperature limit. This work, detailed in a recent letter, addresses fundamental questions about the limits of superconducting critical temperatures and whether coupling to external systems can overcome those boundaries.

The research establishes a phase diagram where enhanced superconductivity arises from bosons existing in either a condensed or thermal state, demonstrating a nontrivial dependence of critical temperature on boson mass. Initially, increasing boson mass strengthens interactions that mediate superconductivity; however, beyond a certain point, the enhancement weakens, eventually returning to the original critical temperature.

This behavior echoes observations in studies of Fermi polarons, where a significant mass imbalance leads to increased dressing of the polaron, suggesting a common underlying mechanism. Without a self-consistent feedback loop between key parameters, the calculations would predict an unphysical, continually increasing critical temperature, highlighting the importance of the chosen renormalization group approach. The study’s findings stem from an investigation into how strongly coupling a superconductor to thermal bosons affects its critical temperature, specifically exploring whether a purely thermal medium can induce enhancement and if existing bounds on critical temperature can be surpassed.

Researchers used a renormalization group approach to account for the complex interplay between bosonic and fermionic degrees of freedom, which is an important element in understanding the observed temperature increases. Comparing critical temperatures with and without the addition of bosons, they established the phase diagram illustrating enhanced superconductivity based on the bosons’ state.

Experimental realization of this boson-enhanced superconductivity is potentially achievable in ultracold atomic mixtures featuring overlapping Feshbach resonances, allowing precise control over interactions. Direct measurement of the critical temperature could be performed in rotating paired superfluids or through spectroscopy of the pairing gap, while atom-resolved and momentum-space techniques could reveal the enhanced correlations predicted by the theory. The self-consistent renormalization group framework predicts a robust increase of the critical temperature across a wide range of interactions.

Heterobilayers of transition metal dichalcogenides (TMDs) coupled to a superconducting layer of twisted bilayer graphene represent a promising platform for testing these predictions, given the current state of experimental capabilities. “We have shown that the coupling of a superconductor to a thermal boson bath can lead to a robust increase of the SC temperature T_c,” the authors state in their conclusion.

“In this way, $T_{c}$ can reach more than twice of its bare value at moderate fermion coupling.” While the enhancement diminishes in strongly-coupled fermion systems, the possibility of significantly boosting critical temperatures through bosonic coupling remains a compelling area for future research and material design.

Functional Renormalization Group Approach to Boson-Fermion Interactions

A renormalization group approach reveals how competition between density fluctuations and boson-induced attraction governs the enhancement of superconductivity, offering a new theoretical lens for understanding these complex interactions. This framework goes beyond approximations like BCS theory, allowing for the examination of regimes where boson and fermion interactions are strong and lack a clear separation of scales, a condition that demands equal treatment of both types of interaction.

The central tool in this analysis is the Wetterich flow equation, a functional that describes how the effective action of the system evolves with changes in an energy scale. This approach allows for the modeling of how bosons and fermions influence each other, specifically how the coupling between them enhances attractive correlations between fermions and between bosons and fermions alike.

Verification of the attractive nature of these induced interactions was achieved by comparing the results to a weak-coupling effective theory obtained after integrating out the bosons, confirming the theoretical model’s internal consistency. The research demonstrates that the critical temperature at which superconductivity emerges can be significantly boosted by the presence of thermal bosons, with the enhancement most pronounced at strong coupling and intermediate boson-fermion interaction strengths.

Specifically, the team found that the critical temperature can exceed twice its original value, a substantial increase achieved through the influence of these thermal bosons. The self-consistency of the renormalization group framework is important, as omitting the feedback loop between the boson-fermion coupling and the boson self-energy would predict an unphysical, continuously increasing critical temperature even as the boson mass becomes infinitely large.

The establishment of a phase diagram further clarifies the conditions under which boson-enhanced superconductivity occurs, differentiating between scenarios where bosons are in a condensed state versus a thermal state. This diagram illustrates how the state of the bosons, whether they form a coherent condensate or remain as individual thermal excitations, impacts the overall superconducting behavior.

Phase Diagram for Enhanced Superconductivity: Thermal vs. Condensed Bosons

A newly established phase diagram details how the state of bosons, whether condensed or thermal, influences the enhancement of superconductivity. The research demonstrates that a robust increase in critical temperature is achievable across a wide range of interactions when a superconductor couples to these thermal bosons, a finding predicated on a self-consistent renormalization group framework. The study’s analysis reveals a critical limit. The bound of 0.16 in the BEC-BCS crossover cannot be exceeded by coupling fermions to a thermal bosonic bath, directly addressing a central question in the field.

The research extends beyond theoretical modeling, suggesting potential experimental realizations in ultracold atomic Bose-Fermi mixtures and in van der Waals material heterostructures. Specifically, the team points to transition metal dichalcogenides where strongly bound excitons in the condensed phase already act as bosons mediating interactions between fermions, similar to the role of phonons in conventional BCS theory.

However, the work goes beyond these conventional models, exploring the behavior when these bosons become thermal and their de Broglie wavelength becomes comparable to the size of Cooper pairs. The phase diagram itself is parametrized using measures relevant to both cold atom experiments and two-dimensional materials, demonstrating the broad applicability of the findings.

Two-Dimensional Materials and Ultracold Atoms as Experimental Platforms

This subtle relationship moves beyond simple models assuming bosons are solely in one state or another, offering a more complete picture of the conditions needed to maximize superconducting performance. Experimental verification of these predictions is envisioned through two distinct, yet complementary, platforms: ultracold atomic systems and van der Waals material heterostructures. Van der Waals materials present an alternative avenue for realizing and probing these effects.

Specifically, the theory suggests potential implementations using electron-exciton mixtures in heterostructures, where excitons act as the thermal bosons coupling to the superconducting layer. This offers a unique opportunity to observe the predicted enhancement in a solid-state system, bridging the gap between ultracold atom experiments and materials science. The study’s Hamiltonian, expressed with units where Planck’s constant and Boltzmann’s constant equal one, details the interactions between two-component fermions and bosonic particles.

The model assumes attractive, contact interactions of strengths g and λ, respectively, and accounts for the kinetic energy of both fermion and boson species. This detailed description allows for a precise calculation of the critical temperature and its dependence on the interaction parameters. This result clarifies the limits of enhancement achievable through this mechanism and directs future research toward optimizing other parameters.

However, the work also reveals that the underlying physics, particularly the competition between density fluctuations and the build-up of boson-induced attraction, remains important for understanding the behavior of superconducting systems. The extension of the present theory to include the Berezinskii-Kosterlitz-Thouless phase transition may allow for thermally-enhanced superconductivity to be a novel probe of the physics of excitonic insulators.

Interplay of Scales Defining Superconducting Critical Temperature

The critical temperature of a superconductor can be substantially increased through interaction with thermal bosons, a self-consistent renormalization group framework predicts, with some instances showing more than a doubling of the baseline temperature at moderate fermion coupling. This enhancement is not limitless, however, as the theoretical model reveals a complex interplay between the bosons and the underlying fermionic system, establishing a phase diagram dependent on the bosons’ state, either condensed or thermal.

This approach allowed for a precise examination of how the addition of bosons alters the superconducting critical temperature across a range of fermionic scattering lengths, revealing a robust increase across the entire spectrum. The model’s predictions are supported by comparisons to systems without bosons, clearly illustrating the enhancement effect.

The study establishes that the extent of temperature increase is suppressed as the original superconductor approaches its inherent bound on the ratio of critical temperature to Fermi temperature, T_c/T_F, near the unitary limit. The team’s analysis also highlights the importance of considering the boson density, demonstrating that the critical temperature’s behavior is significantly influenced by this parameter.

These materials offer a promising platform for observing and manipulating the predicted effects. The team’s findings, while based on a simplified model, provide a valuable framework for understanding and optimizing superconducting properties through external manipulation of the bosonic environment.

👉 More information
🗞 Enhancing superconductivity using thermal bosons
✍️ Ekaterina Vlasiuk, Manfred Salmhofer, Eugene Demler and Richard Schmidt
🧠 DOI: http://link.aps.org/doi/10.1103/vth5-lzjn

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