Thin Superconducting Films as Reflectors for High-$Q$ Terahertz Fabry–Pérot Resonators

Abstract

In this article, we fabricate Fabry–Pérot resonators by depositing superconducting Mo$_{0.6}$Re$_{0.4}$ films with thicknesses of 10, 20, and 30 nm (critical temperatures $T_{c} = 6.7$, 7.4, and 7.7 K, respectively) on both sides of plane-parallel slabs of highly resistive silicon. Using time-domain and coherent source spectroscopy, we determine the terahertz spectra of the complex ac conductivity and dielectric permittivity of the films from the measured transmission coefficient spectra of the resonators in the range of 3–50 cm$^{-1}$ (90 GHz to 1.5 THz) at temperatures of 2.5–300 K. The obtained frequency and temperature dependences of the conductivity and permittivity spectra are well described by the Bardeen–Cooper–Schrieffer (BCS) theory within single-gap approximation. We extract and analyze the temperature dependencies of the superconducting energy gap, the London penetration depth, and the superconducting condensate plasma frequency. The ratio $2\Delta (0)/k_{B} T_{c} \approx 4.05$ is found to be slightly higher than the BCS weak-coupling value of 3.52, indicating a moderately strong coupling regime in the studied Mo$_{0.6}$Re$_{0.4}$ films. The critical temperature $T_{c}$ and the zero-temperature superconducting energy gap $2\Delta (0)$ are found to decrease with decreasing film thickness, a behavior that is associated with the reduction of the superconducting order parameter due to the contribution of surface states to the free energy. The dramatic increase in the reflectivity of the Mo$_{0.6}$Re$_{0.4}$ films and drop in losses in the superconducting state lead to a significant improvement in the performance of the Fabry–Pérot resonators, expressed in the enhanced quality factor $Q$ and the finesse $F$ of the interferometric resonances. For example, at $T = 2.5$ K, the resonator with the 30-nm-thick films exhibits $Q = 830$ (resonances at 5.8 and 8.8 cm$^{-1}$) and $F = 580$ (resonance at $\approx 3$ cm$^{-1}$; full width at half maximum $= 0.005$ cm$^{-1}$, or 150 MHz). Due to its compactness, simple design, and high quality, the resonator is a promising candidate for applications in modern terahertz technology.