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arXiv:2610.40222

Stabilizing fluctuating Cooper pairs with a terahertz resonator

Frieder Lindel, Jonathan B. Curtis, Jérôme Faist, Eugene Demler

cond-mat.mes-hallquant-phSubmitted Oct 29, 2026• Announced Oct 30, 2026
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Abstract

Coupling quantum materials to electromagnetic cavities or resonators without external driving has gained prominence as a new control mechanism. Here we develop an equilibrium theory of a mesoscopic, disordered two-dimensional superconductor coupled to a subwavelength terahertz resonator, focusing on the interplay between superconducting phase fluctuations in the sample and electromagnetic fluctuations of the resonator. Modeling the resonator as a lumped-element circuit, we show that the coupling enhances, rather than suppresses, the superconducting transition temperature $T_c$. When the sample is smaller than the Pearl length, phase fluctuations near the Berezinskii--Kosterlitz--Thouless (BKT) transition strongly amplify this enhancement. Crucially, the resistive quasiparticle response of the sample must be included in the analysis: at low frequencies the superfluid shunts the normal-fluid channel, reducing the total sample impedance. For representative parameters, a $1 \,μ\mathrm{m} \times 1 \,μ\mathrm{m}$, $8 $nm-thick disordered film, we find a relative $T_c$ enhancement of about $1\%$, an order of magnitude larger than the $0.1\% $ obtained when phase fluctuations are neglected. These results identify superconductors with soft phase fluctuations as promising platforms for equilibrium control with terahertz resonators.

AI Summary

Can an undriven terahertz resonator enhance superconductivity by modifying equilibrium electromagnetic fluctuations, particularly near a phase-fluctuation-driven transition? This paper models a mesoscopic, disordered two-dimensional superconducting film coupled in series to a lumped-element $LC$ resonator. Integrating out the circuit and dissipative bath gives an impedance-dependent free energy, which is added to a Ginzburg–Landau functional and minimized over the superfluid density. BKT fluctuations are incorporated through finite-size Kosterlitz renormalization-group flows. Including the resistive normal-fluid channel reverses the suppression predicted when only the condensate response is retained: superconductivity shunts the normal resistance, lowering the circuit contribution to the free energy. For a $1\,\mu\mathrm{m}\times1\,\mu\mathrm{m}$, $8$-nm-thick film with sheet conductivity $0.64e^2/\hbar$ and coherence length $10$ nm, the model predicts approximately $1\%$ enhancement of the finite-size transition temperature with BKT fluctuations, versus roughly $0.1\%$ without them. BKT enhancement reaches this scale at $\Omega_{\rm LC}\simeq6.7T_{\rm BCS}$, corresponding to terahertz frequencies for kelvin-scale transitions. The single-mode effect decreases with sample area; fluctuations soften, but do not remove, this suppression. The analysis assumes a sample smaller than the Pearl length and uses static, sample-scale renormalized stiffness in a two-fluid optical response, leaving dynamical vortex response untreated. A microscopic Zimmermann-conductivity check preserves the positive mean-field shift but reduces its magnitude to $20$–$40\%$ of the two-fluid prediction. The required disorder does not match existing cleaner-film experiments. Including vortex free energy also introduces unresolved variational ambiguities and potentially discontinuous transitions.

No sign of AI-generated textStrong assumptionsPossible error

Central claim may not hold: The predicted BKT amplification uses static, sample-scale vortex screening at nonzero Matsubara frequencies without establishing the required dynamical superconducting response. The main BKT calculation omits vortex free energy from its variational functional, while the alternative treatment changes the enhancement and produces an unresolved sharp transition. A microscopic conductivity model reduces the bare-BCS enhancement to approximately 0.2–0.4 of the two-fluid result, and the quoted 1% BKT enhancement has not undergone a corresponding robustness test.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

Comments
10 pages, 6 figures

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Coupling quantum materials to electromagnetic cavities or resonators without external driving has gained prominence as a new control mechanism. Here we develop an equilibrium theory of a mesoscopic, disordered two-dimensional superconductor coupled to a subwavelength terahertz resonator, focusing on the interplay between superconducting phase fluctuations in the sample and electromagnetic fluctuations of the resonator. Modeling the resonator as a lumped-element circuit, we show that the coupling enhances, rather than suppresses, the superconducting transition temperature TcT_cTc​. When the sample is smaller than the Pearl length, phase fluctuations near the Berezinskii--Kosterlitz--Thouless (BKT) transition strongly amplify this enhancement. Crucially, the resistive quasiparticle response of the sample must be included in the analysis: at low frequencies the superfluid shunts the normal-fluid channel, reducing the total sample impedance. For representative parameters, a 1 μm×1 μm1 \,μ\mathrm{m} \times 1 \,μ\mathrm{m}1μm×1μm, 88 8nm-thick disordered film, we find a relative TcT_cTc​ enhancement of about 1%1\%1%, an order of magnitude larger than the 0.1%0.1\% 0.1% obtained when phase fluctuations are neglected. These results identify superconductors with soft phase fluctuations as promising platforms for equilibrium control with terahertz resonators.
Can an undriven terahertz resonator enhance superconductivity by modifying equilibrium electromagnetic fluctuations, particularly near a phase-fluctuation-driven transition? This paper models a mesoscopic, disordered two-dimensional superconducting film coupled in series to a lumped-element LCLCLC resonator. Integrating out the circuit and dissipative bath gives an impedance-dependent free energy, which is added to a Ginzburg–Landau functional and minimized over the superfluid density. BKT fluctuations are incorporated through finite-size Kosterlitz renormalization-group flows.
Including the resistive normal-fluid channel reverses the suppression predicted when only the condensate response is retained: superconductivity shunts the normal resistance, lowering the circuit contribution to the free energy. For a 1 μm×1 μm1\,\mu\mathrm{m}\times1\,\mu\mathrm{m}1μm×1μm, 888-nm-thick film with sheet conductivity 0.64e2/ℏ0.64e^2/\hbar0.64e2/ℏ and coherence length 101010 nm, the model predicts approximately 1%1\%1% enhancement of the finite-size transition temperature with BKT fluctuations, versus roughly 0.1%0.1\%0.1% without them. BKT enhancement reaches this scale at ΩLC≃6.7TBCS\Omega_{\rm LC}\simeq6.7T_{\rm BCS}ΩLC​≃6.7TBCS​, corresponding to terahertz frequencies for kelvin-scale transitions. The single-mode effect decreases with sample area; fluctuations soften, but do not remove, this suppression.
The analysis assumes a sample smaller than the Pearl length and uses static, sample-scale renormalized stiffness in a two-fluid optical response, leaving dynamical vortex response untreated. A microscopic Zimmermann-conductivity check preserves the positive mean-field shift but reduces its magnitude to 202020–40%40\%40% of the two-fluid prediction. The required disorder does not match existing cleaner-film experiments. Including vortex free energy also introduces unresolved variational ambiguities and potentially discontinuous transitions.
Superconductors carry electrical current without resistance when paired electrons condense into a coherent macroscopic quantum state. In underdoped cuprates, evidence suggests that pairing-related correlations and superconducting fluctuations can survive above the temperature at which global coherence is lost, pointing to phase fluctuations as a key limitation on superconductivity in this regime. Motivated by recent demonstrations of cavity-modified collective states in quantum materials, we investigate whether superconducting coherence can be stabilized by engineering the electromagnetic environment of the superconductor. We study an underdoped YBa2_22​Cu3_33​O7−δ_{7-δ}7−δ​ thin film in a tunable terahertz cavity formed with a semi-transparent gold mirror. From temperature-dependent terahertz transmission measurements, we find that the cavity enhances the superconducting response below the critical temperature, with an increase of the inferred superfluid weight. The effect becomes more pronounced at smaller cavity lengths and is accompanied by an upward shift of the superconducting onset temperature. Calculations based on a cavity-coupled model for phase-fluctuating superconductors capture these trends and support an interpretation in terms of cavity-enhanced phase stiffness. These results showcase the potential of cavity engineering for designing emergent functionalities in correlated systems.
We study the phase fluctuations in the normal state of generic two-dimensional superconducting systems with sss-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the two-dimensional Berezinskii-Kosterlitz-Thouless transition lead to a significant broadening of the single-particle spectrum, giving birth to the pseudogap phenomenon. Quantitatively, the broadening of spectral weights near the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the fermionic attractive-UUU Hubbard model on the square lattice, using the unbiased determinant quantum Monte Carlo method and stochastic analytic continuation.
Driving a conventional superconductor with an appropriately tuned classical electromagnetic field can lead to an enhancement of superconductivity via a redistribution of the quasiparticles into a more favorable nonequilibrium distribution-a phenomenon known as the Eliashberg effect. Here, we theoretically consider coupling a two-dimensional superconducting film to the quantized electromagnetic modes of a microwave resonator cavity. As in the classical Eliashberg case, we use a kinetic equation to study the effect of the fluctuating, dynamical electromagnetic field on the Bogoliubov quasiparticles. We find that when the photon and quasiparticle systems are out of thermal equilibrium, a redistribution of quasiparticles into a more favorable nonequilibrium steady state occurs, thereby enhancing superconductivity in the sample. We predict that by tailoring the cavity environment (e.g., the photon occupation and spectral functions), enhancement can be observed in a variety of parameter regimes, offering a large degree of tunability.
We consider the attractive Hubbard model with on-site disorder as a prototype of a disordered superconductor. We solve the Bogoliubov-de Gennes equations on two-dimensional finite clusters at zero temperature and evaluate the electromagnetic response to a vector potential. We find that the standard decoupling between transverse and longitudinal response does not apply in the presence of disorder. Moreover, the superfluid density is strongly reduced by the relaxation of the phase of the order parameter already at mean-field level when disorder is large. We also find that the anharmonicity of the phase fluctuations is strongly enhanced by disorder. Beyond mean field, this provides an enhancement of quantum fluctuations inducing a zero-temperature transition to a nonsuperconducting phase of disordered preformed pairs. Finally, the connection of our findings with the glassy physics for extreme dirty superconductors is discussed.
In this thesis, we first demonstrate that a disordered superconductor with high kinetic inductance can realise a microwave low-loss, non-dissipative circuit element with impedance greater than the quantum resistance. This element, known as a superinductor, can suppress the fluctuations of charge in a quantum circuit.For this purpose, we fabricated and characterised 20 nm thick, 40 nm wide niobium-nitride nanowires and determined the impedance to 6.795 kΩ. We demonstrate internal quality factors Qi = 2.5e4 in nanowire resonators at single photon excitation, which is significantly higher than values reported in devices with similar materials and geometries. Moreover, we show that the dominant dissipation in our nanowires is not an intrinsic property of the disordered films, but can instead be fully understood within the framework of two-level systems.To further characterise these losses, we then explore the geometrical scaling, toward nanowire dimensions, of dielectric losses in superconducting microwave resonators fabricated with the same techniques and from the same NbN thin-film as the nanowire superinductors. For this purpose, we perform an experimental and numerical study of dielectric loss at low temperatures. Using 3D finite-element simulation of the Maxwell--London equations, we compute the geometric filling factors of the lossy regions in our resonator structures and fit the experimental data to determine the intrinsic loss tangents of its interfaces and dielectrics. Finally, we study the effect of two-level systems on the performance of various superconducting quantum circuits. For this purpose, we measure coherence-time fluctuations in qubits and frequency fluctuations in resonators. In all devices, through statistical analysis, we identify the signature of individual Lorentzian fluctuators in the noise. We find that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems. Furthermore, when examining the low-frequency noise of three different types of superconducting resonator - one NbN nanowire, one Al coplanar waveguide, and one Al 3D cavity - we observe a similar power-law dependence of the Lorentzian switching time and amplitude on the circulating power in the resonators, suggesting a common noise mechanism in the three different types of devices.
Vacuum-dressed superconductivity in NbN observed in a high-QQQ terahertz cavity
Emerging theoretical frameworks suggest that physical properties of matter can be altered within an optical cavity by harnessing quantum vacuum electromagnetic fluctuations, even in the total absence of external driving fields. Among the most intriguing predictions is the potential to noninvasively manipulate superconductivity. Here, we experimentally observe modified superconductivity in niobium nitride (NbN) thin films within high-quality-factor (QQQ) terahertz cavities. Using terahertz time-domain spectroscopy, we characterize the NbN response both in free space and within a high-QQQ photonic-crystal cavity. Our analysis reveals significant cavity-induced modifications to the optical conductivity. A theoretical model indicates that these changes originate from a substantial (∼13 %\sim13\,\%∼13%) reduction in the superfluid density and a minor (∼2 %\sim2\,\%∼2%) reduction in the superconducting gap, driven by cavity vacuum fluctuations. These results demonstrate a platform for engineering ground states via vacuum--matter coupling, opening frontiers in cavity materials science.