Optical conductivity of superconducting K${}_{0.8}$Fe${}_{2-y}$Se${}_2$ single crystals: Evidence for a Josephson-coupled phase

The optical properties of the iron-chalcogenide superconductor K${}_{0.8}$Fe${}_{2-y}$Se${}_2$ with a critical temperature $T_c=31$ K have been measured over a wide frequency range in the $\mathit{ab}$ planes above and below $T_c$. The conductivity is incoherent at room temperature but becomes coherent (Drude-like) at $T\gtrsim T_c$; however, $R_{\square }\simeq 320$ k$\Omega$, well above the threshold for the superconductor-insulator transition at $R_{\square }=h/4e^2\simeq 6.9$ k$\Omega$. Below $T_c$, the superfluid density ${\rho }_{s0}\simeq 48\times {10}^3$ cm${}^{-2}$ places this material on the scaling line ${\rho }_{s0}/8\simeq 4.4{\sigma }_{dc}{T}_c$, but in a region associated with Josephson coupling, suggesting this material is inhomogeneous and constitutes a Josephson phase.

Figure 1

The absolute reflectance over a wide frequency range for a cleaved single crystal of K${}_{0.8}$Fe${}_{2-y}$Se${}_2$ for light polarized in the $\mathit{ab}$ planes at several temperatures above and below $T_c$. Inset: The unit cell in the $I4/m$ space group.

Figure 2

The real part of the optical conductivity in the low-frequency region for K${}_{0.8}$Fe${}_{2-y}$Se${}_2$ for light polarized in the $\mathit{ab}$ planes for several temperatures above and below $T_c=31$ K. The polygons at the origin denote the values for the conductivity determined from transport measurements on a crystal from the same batch. Inset: Drude-Lorentz fit to the conductivity at 35 K.

Figure 3

The real part of the optical conductivity for light polarized in the $\mathit{ab}$ planes of K${}_{0.8}$Fe${}_{2-y}$Se${}_2$ over a wide frequency range for several temperatures above and below $T_c$. Two previously observed features are labeled $\alpha$ and $\beta$; two further features at low and high frequencies are denoted as $\gamma$ and $\delta$, respectively. Inset: The detailed behavior of the $\gamma$ feature.

Figure 4

The log-log plot of the spectral weight of the superfluid density $N_c\equiv {\rho }_{s0}/8$ vs ${\sigma }_{dc}{T}_c$ in the $\mathit{ab}$ planes for a variety of electron- and hole-doped cuprates compared with BaFe${}_{1.85}$Co${}_{0.15}$As${}_2$,[29] FeTe${}_{0.55}$Se${}_{0.45}$,[30] and K${}_{0.8}$Fe${}_{2-y}$Se${}_2$ (this work), highlighted by the circles. The dashed line corresponds to the general result for the cuprates ${\rho }_{s0}/8\simeq 4.4{\sigma }_{dc}{T}_c$, while the dotted line denotes the region of the scaling relation typically associated with Josephson coupling along the $c$ axis.