Optical investigations of chemically pressurized ${\mathrm{EuFe}}_2$(${\mathrm{As}}_{1-x}{\mathrm{P}}_x$)${}_2$: An $s$-wave superconductor with strong interband interactions

Superconducting ${\mathrm{EuFe}}_2$(${\mathrm{As}}_{0.82}{\mathrm{P}}_{0.18}$)${}_2$ single crystals are investigated by broad-band infrared spectroscopy. Below $T_c=28$ K, a superconducting gap forms at $2{\Delta }_0=9.5\hspace{0.5em}\mathrm{meV}=3.7k_B{T}_c$, causing the reflectivity to sharply rise to unity at low frequency. In the range of the gap, the optical conductivity can be perfectly described by BCS theory with an $s$-wave gap and no nodes. From our analysis of the temperature-dependent conductivity and spectral weight at $T>T_c$, we deduce an increased interband coupling between hole and electron sheets on the Fermi surface when $T$ approaches $T_c$.

Figure 1

Optical properties of EuFe${}_2$(As${}_{0.82}$P${}_{0.18}$)${}_2$ in the $\mathit{ab}$ plane measured in a broad frequency range at different temperatures. (a), (b) The reflectivity $R(\omega )$ increases with a change of curvature around 100 cm${}^{-1}$ for $T<28$ K and approaches unity at 74 cm${}^{-1}$, which is a signature for a superconducting gap formation. Inset: in-plane dc resistivity. The superconducting transition occurs at $T=28$ K, where $\rho (T)$ sharply decreases to zero. (c) Below 28 K, the sudden drop of ${\sigma }_1(\omega )$ to zero indicates a nodeless $s$-wave superconducting gap. (d) Drude-Lorentz fit for the normal-state conductivity ($T=30$ K). (e) In the normal state, ${\sigma }_1(\omega )$ develops as a metal upon cooling. (f) Ratio of ${\sigma }_1(\omega )$ in the normal ($T=30$ K) and superconducting states ${\sigma }_1^{(s)}(\omega )/{\sigma }_1^{(n)}(\omega )$ of EuFe${}_2$(As${}_{0.82}$P${}_{0.18}$)${}_2$ at $T=5$ K. The dashed red line corresponds to the fit by the BCS model using a single gap of $2{\Delta }_0=74$ cm${}^{-1}$, while the dashed gray line refers to the two-gap scenario with $2{\Delta }_N=150$ cm${}^{-1}$ and $2{\Delta }_B=74$ cm${}^{-1}$. (g) Penetration depth as a function of temperature plotted in a renormalized fashion. The experimental data of EuFe${}_2$(As${}_{0.82}$P${}_{0.18}$)${}_2$ can be described with $1-(T/T_c){}^4$.

Figure 2

Fermi sheets in first Brillouin zone for $M$Fe${}_2$As${}_2$ family ($M$ $=$ Ba, Eu, Sr). Three sheets at the $\Gamma$ point are holelike Fermi surfaces, and two at the M point are electronlike Fermi surfaces. (a) Parent compound $M$Fe${}_2$As${}_2$; (b) hole doping leads to a change in the diameter of the Fermi surface in $M_{1-x}$K${}_x$Fe${}_2$As${}_2$. The large gap $2{\Delta }_0=7.5k_B{T}_c$ opens at the inner two hole-FSs (red sheets) and two electron-FSs (green sheets), while the small gap $2{\Delta }_0=3.7k_B{T}_c$ opens at the outer hole-FS (blue sheet). (c) P substitution in $M$Fe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ changes the warping of the Fermi surface and thus reduces the two-dimensional character.

Figure 3

(a) The spectral weight $\mathrm{SW}({\omega }_c)=8{\int }_0^{{\omega }_c}{\sigma }_1(\omega )\mathrm{d}\omega$ as a function of cutoff frequency ${\omega }_c$ for several temperatures. (b) The normalized spectral weight SW$(T)$/SW(300 K). A minimum can be found at ${\omega }_{\min }\approx 3000$ cm${}^{-1}$. (c) The spectral weight for the mid-infrared component $\alpha$-Lorentz and the Drude component plotted as a function of temperature for $T>T_c$.