Optical conductivity of superconducting ${\mathbf{Rb}}_{\mathbf{2}}{\mathbf{Fe}}_{\mathbf{4}}{\mathbf{Se}}_{\mathbf{5}}$ single crystals

We report the complex dielectric function of high-quality nearly-stoichiometric ${\mathrm{Rb}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ single crystals with $T_{\mathrm{c}}=32\mathrm{K}$ determined by wide-band spectroscopic ellipsometry and time-domain transmission spectroscopy in the spectral range of $1\mathrm{meV}\le \hslash \omega \le 6.5\mathrm{eV}$ at temperatures of $4\mathrm{K}\le T\le 300\mathrm{K}$. This compound simultaneously displays a superconducting and a semiconducting optical response. It reveals a direct band gap of $\approx 0.45\mathrm{eV}$ determined by a set of spin-controlled interband transitions. Below 100 K, in the lowest terahertz spectral range, we observe a clear metallic response characterized by the negative dielectric permittivity ${\varepsilon }_1$ and bare (unscreened) ${\omega }_{\mathrm{pl}}\approx 100\mathrm{meV}$. At the superconducting transition, this metallic response exhibits a signature of a superconducting gap below 8 meV. Our findings suggest a coexistence of superconductivity and magnetism in this compound as two separate phases.

Figure 1

(a) Imaginary and (b) real parts of the dielectric function of RFS in the $0.01–6.5\mathrm{eV}$ spectral range at different temperatures. [Inset in (a)] Plot of ${\left[{\varepsilon }_2\left(\omega \right){\omega }^2\right]}^2$ near the absorption edge. The intersection of the dashed line with the energy axis defines the direct energy gap ${\Delta }_{\mathrm{dir}}=0.45\mathrm{eV}$ at $12\mathrm{K}$. [Inset in (b)] Temperature dependence of ${\epsilon }_2\left(0.53\mathrm{eV}\right)$.

Figure 2

(a) Imaginary and (b) real parts of the dielectric function of RFS in the THz spectral region obtained via the time-domain transmission spectroscopy. The blue arrow marks a low-energy electronic excitation. Thick gray lines show a Drude fit to ${\varepsilon }_1\left(\omega \right)$ and ${\varepsilon }_2\left(\omega \right)$ as described in the text. (Inset) Electric-field transients transmitted through a $25-\mu \mathrm{m}$-thick superconducting sample (scaled by 10, red line) and a $100-\mu \mathrm{m}$-thick transparent insulating sample (blue line). The dashed line plots the reference signal.

Figure 3

Difference spectra (a) ${\sigma }_1(T,\omega )-{\sigma }_1(4\mathrm{K},\omega )$ and (b) ${\varepsilon }_1(T,\omega )-{\varepsilon }_1(4\mathrm{K},\omega )$ of a $25-\mu \mathrm{m}$ superconducting sample. The blue arrow marks the same low-energy electronic excitation as in Fig. 2a. Kramers-Kronig transformation of the difference spectrum $\Delta {\sigma }_1^{36–12\mathrm{K}}\left(\omega \right)$ [cyan line in (a)] with (circles) and without (triangles) the superconductivity-induced term $8A/{\omega }^2$. The shaded area indicates the spectral weight used to estimate the ${\omega }_{\mathrm{pl}}$ of the superconducting condensate (see text). (c) Temperature dependence of the time-domain transmission phase and (d) its temperature derivative for several frequencies. Superconducting transition temperature of 32 K (dashed line).

Figure 4

(Left panels) Comparison of the experimentally obtained real parts of the (a) optical conductivity and (b) dielectric function of an optimally doped BKFA at 12 K and RFS at 300 and 12 K. (Right panels) Same as in left panels as obtained in LDA calculations. The arrows in (a) and (c) indicate the narrow low-energy optical bands that can be resolved at low temperatures in RFS but not BKFA.