Nonequilibrium Quasiparticle Dynamics in a MoRe-Based Superconducting Resonator under IR Excitation

The response of a MoRe-based superconducting resonator operating near 5 K to pulsed infrared irradiation is investigated, and the underlying physical mechanisms are analyzed. The device exhibits a pronounced nonlinear response dominated by nonequilibrium quasiparticle dynamics rather than uniform thermal heating. Infrared pulses produce strong distortions of the resonance curve and a transient decrease in the resonance frequency, consistent with increased kinetic inductance caused by quasiparticle generation. The frequency shift scales approximately linearly with absorbed power, whereas the dissipation response saturates at higher powers, indicating the formation of a nonequilibrium steady-state quasiparticle population. These observations demonstrate a transition from a linear pair-breaking regime to a saturated dissipation regime, likely associated with a quasiparticle relaxation bottleneck or partial suppression of the smaller superconducting gap in MoRe. The results highlight the relevance of nonequilibrium processes in MoRe and confirm its potential for microwave kinetic-inductance detector applications.

💡 Research Summary

This paper investigates the nonequilibrium quasiparticle response of a molybdenum‑rhenium (MoRe) superconducting microstrip resonator when illuminated with pulsed infrared (IR) radiation. The resonator, fabricated from a 60 nm MoRe film on sapphire and patterned into a λ/2 fractal geometry (≈3 mm × 3 mm, 20 µm line width), operates at a bath temperature of 4.6 K. Infrared excitation is provided by a miniature incandescent lamp placed 7.5 mm from the device; the lamp is driven by current pulses of variable duration (10 ms to 100 ms) at a repetition rate of 1 Hz. By recording the lamp voltage and current during each pulse, the filament temperature and consequently the incident IR power density P_s(t) are reconstructed (accounting for filter transmission and geometric factors). The resonator is probed in a two‑port configuration with a vector network analyzer at a low microwave probe power (–36 dBm) to stay within the linear regime.

Amplitude‑frequency sweeps performed while the IR pulses are active reveal a clear evolution of the resonance curve. For short pulses (≤10 ms) the curve is essentially unchanged, reflecting negligible absorbed power during the initial heating phase of the filament. As pulse duration increases, the resonance becomes increasingly distorted: a sharp dip appears on the low‑frequency side and a corresponding bump on the high‑frequency side, indicating a transient reduction of the resonance frequency f₀ during illumination. Time‑domain measurements at a fixed probe frequency (f = f₀) show a rapid drop in the transmission magnitude |S₂₁| coincident with the IR pulse, followed by a slow recovery that extends beyond the pulse because the filament remains hot (≈400 K) for tens of milliseconds.

From the complex transmission data the authors extract the instantaneous resonance frequency shift Δf₀(t) and the change in internal quality factor 1/Q₀(t). The frequency shift scales approximately linearly with the absorbed IR power density, consistent with a simple two‑fluid picture where each absorbed photon with energy ℏω > 2Δ breaks a Cooper pair and creates a nonequilibrium quasiparticle population n_ex. In steady state, n_ex = κ P_s τ_r, where κ is a conversion factor and τ_r the quasiparticle recombination time. Because the kinetic inductance L_k ∝ λ² ∝ 1/n_s (with n_s the superfluid density), the increase of n_ex reduces n_s, enlarges λ, and raises L_k, thereby lowering f₀. The measured linear Δf₀–P_s relationship yields an effective κ_ex = κ τ_r, from which τ_r is inferred to be on the order of tens of microseconds.

In contrast, the dissipation response (1/Q₀) exhibits saturation for pulse durations longer than ~70 ms. This behavior is interpreted as a quasiparticle‑relaxation bottleneck: as n_ex grows, recombination processes become limited, and additional absorbed photons no longer increase the loss. The authors liken this to a “quasiparticle bottleneck” or “relaxation bottleneck” that is characteristic of multigap superconductors. MoRe is known to possess a larger primary gap and a smaller secondary gap; the latter may dominate the low‑energy quasiparticle dynamics and thus set the recombination time scale.

To separate genuine nonequilibrium effects from simple heating, the authors independently measured the temperature dependence of f₀(T) and 1/Q₀(T) in the absence of illumination. By mapping the observed Δf₀(t) and Δ(1/Q₀)(t) onto these calibration curves, they derive effective temperature rises ΔT_f (from frequency) and ΔT_Q (from loss). For a 10 ms pulse at P_s ≈ 340 µW mm⁻², ΔT_f ≈ 0.035 K while ΔT_Q ≈ 0.87 K, i.e., the loss‑derived temperature increase is more than an order of magnitude larger than the frequency‑derived one. This discrepancy demonstrates that the dominant mechanism is not uniform heating of the film but the generation of a nonequilibrium quasiparticle population that strongly enhances microwave loss.

The paper concludes that MoRe fractal resonators exhibit a clear transition from a linear pair‑breaking regime (where frequency shift follows absorbed power) to a saturated dissipation regime (where loss is limited by quasiparticle recombination). These findings confirm that MoRe, with its relatively high critical temperature (~8 K), sizable kinetic inductance, and manageable quasiparticle dynamics, is a promising material for microwave kinetic‑inductance detectors (MKIDs) operating at a few kelvin. The authors suggest future work to (i) probe the recombination dynamics more directly (e.g., with pump‑probe spectroscopy), (ii) explore the role of the secondary superconducting gap, and (iii) optimize fractal geometries to increase pixel density while minimizing inter‑pixel coupling. Overall, the study provides a comprehensive experimental and theoretical framework for understanding and exploiting nonequilibrium quasiparticle effects in MoRe‑based superconducting resonators.