Optical Properties of Superconducting K$_{0.8}$Fe$_{1.7}$(Se$_{0.73}$S$_{0.27}$)$_2$ Single Crystals

TL;DR

The paper investigates the optical properties of the superconducting K0.8Fe1.7(Se0.73S0.27)2 single crystals in the ab plane over 4–300 K using infrared spectroscopy and spectroscopic ellipsometry. It applies a one-Drude-Lorentz model to the normal-state response and analyzes the superconducting state by extracting the gap, superconducting plasma frequency, and penetration depth. The results reveal a SC gap of $2Δ(5K)=11.8$ meV and a SC plasma frequency $ω_{pl,s}=213±5$ cm^-1, corresponding to a penetration depth of $λ=7.5±0.2$ μm, with the superconducting phase occupying ≤25% of the sample, consistent with a percolative, phase-separated state. These findings illuminate the bulk electrodynamics of iron-selenide superconductors and provide benchmarks for percolative superconductivity in phase-separated systems.

Abstract

The optical properties of the superconducting K$_{0.8}$Fe$_{1.7}$(Se$_{0.73}$S$_{0.27}$)$_2$ single crystals with a critical temperature $T_c\approx 26$ K have been measured in the {\it ab} plane in a wide frequency range using both infrared Fourier-transform spectroscopy and spectroscopic ellipsometry at temperatures of 4--300 K. The normal-state reflectance of K$_{0.8}$Fe$_{1.7}$(Se$_{0.73}$S$_{0.27}$)$_2$ is analyzed using a Drude-Lorentz model with one Drude component. The temperature dependences of the plasma frequency, optical conductivity, scattering rate, and dc resistivity of the Drude contribution in the normal state are presented. In the superconducting state, we observe a signature of the superconducting gap opening at $2Δ$(5~K) = 11.8~meV. An abrupt decrease in the low-frequency dielectric permittivity $\varepsilon _1(ω)$ at $T < T_c$ also evidences the formation of the superconducting condensate. The superconducting plasma frequency $ω_{pl,s} = (213\pm 5)$~cm$^{-1}$ and the magnetic penetration depth $λ=(7.5\pm 0.2)$~$μ$m at $T=5$~K are determined.

Figures (5)

• Figure 1: (Color online) The absolute reflectance for K$_{0.8}$Fe$_{1.7}$(Se$_{0.73}$S$_{0.27}$)$_2$ single crystal for light polarized in the ab plane at several temperatures above and below $T_c$.
• Figure 2: (Color online) The real part of the optical conductivity of K$_{0.8}$Fe$_{1.7}$(Se$_{0.73}$S$_{0.27}$)$_2$ at 30 K over a broad frequency range (dots) together with the Lorentz contributions revealed by the Drude-Lorentz analysis. The red solid curve is a total contour.
• Figure 3: (Color online) The expanded plots of $\sigma _1(\omega )$ spectra below 300 cm$^{-1}$ taken at 300 K (a), 100 K (b), 30 K (c), and 5 K (d) as well as the results of Drude-Lorentz fit to the conductivity of K$_{0.8}$Fe$_{1.7}$(Se$_{0.73}$S$_{0.27}$)$_2$. The Lorentz contributions are shown in gray. The inset in Fig. 3(d) shows a part of the $\sigma _1(\omega )$ data in the region of the SC gapping.
• Figure 4: (Color online) The spectra of the dielectric permittivity of K$_{0.8}$Fe$_{1.7}$(Se$_{0.73}$S$_{0.27}$)$_2$ at various temperatures (points) and the fit of the spectra with the expression $\varepsilon _1(\omega )\propto -(\omega _{pl,s}/\omega)^2$ (black lines). The inset (a) shows the temperature dependence of the SC gap while the inset (b) displays the temperature dependences of the SC plasma frequency and the magnetic penetration depth.
• Figure 5: (Color online) The model parameters $\omega _{pl}$, $\gamma$, $\sigma _1$, and $\rho$ of the K$_{0.8}$Fe$_{1.7}$(Se$_{0.73}$S$_{0.27}$)$_2$ single crystals in the normal state as a function of temperature. Blue points in the panel (d) are the results of Van der Pauw measurements.