Interlayer Coherence and Superconducting Condensate in the $c$-Axis Response of Optimally Doped $\mathrm{Ba}({\mathrm{Fe}}_{1\mathbf{-}x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ High-$T_c$ Superconductor Using Infrared Spectroscopy

We report on the infrared studies of the interlayer charge dynamics of a prototypical pnictide superconductor $\mathrm{Ba}({\mathrm{Fe}}_{0.926}{\mathrm{Co}}_{0.074}{)}_2{\mathrm{As}}_2$. We succeeded in probing the intrinsic interlayer response by performing infrared experiments on the crystals with a cleaved $ac$ surface. Our experiments identify the coexistence of the suppression of the electronic spectral weight and the development of a coherent Drude-like response in the normal state. The formation of the interlayer condensate is clearly observed in the superconducting state and appears to be linked to coherent contribution to the normal-state conductivity.

Figure 1

$T$-dependent $c$-axis reflectance spectra $R_c(\omega )$ of $\mathrm{Ba}({\mathrm{Fe}}_{0.926}{\mathrm{Co}}_{0.074}{)}_2{\mathrm{As}}_2$ with $T_c=23\mathrm{K}$. The sharp spike at $108{\mathrm{cm}}^{-1}$ is due to infrared active phonon mode. Upper inset: $R_c(\omega )$ over broad frequency up to $25000{\mathrm{cm}}^{-1}$. Lower inset: the $ab$-plane reflectance $R_{ab}(\omega )$ of OPD $\mathrm{Ba}({\mathrm{Fe}}_{0.92}{\mathrm{Co}}_{0.08}{)}_2{\mathrm{As}}_2$ in the far-infrared region.

Figure 2

(a) Real part of the $c$-axis optical conductivity ${\sigma }_{1c}(\omega )$. The sharp peak at $108{\mathrm{cm}}^{-1}$ is due to infrared active phonon mode. As $T$ decreases, ${\sigma }_{1c}(\omega )$ in the far-infrared frequency region becomes depressed and the suppressed SW is most likely not recovered up to $4000{\mathrm{cm}}^{-1}$, as shown in the inset. The dashed line represents the extrapolated ${\sigma }_{1c}(\omega )$ at $T=27\mathrm{K}$ using the Hagen-Rubens analysis of $R_c(\omega )$. The hatched area denotes the SW of the superconducting condensate. The solid circle, triangle, and rectangle denote the dc conductivity values at 295, 150, and 27 K, respectively (Ref. 5). (b) Real part of the $ab$-plane optical conductivity ${\sigma }_{1ab}(\omega )$ of OPD $\mathrm{Ba}({\mathrm{Fe}}_{0.92}{\mathrm{Co}}_{0.08}{)}_2{\mathrm{As}}_2$ (Ref. 17).

Figure 3

Imaginary part of $c$-axis optical conductivity ${\sigma }_{2c}(\omega )$ of $\mathrm{Ba}({\mathrm{Fe}}_{0.926}{\mathrm{Co}}_{0.074}{)}_2{\mathrm{As}}_2$ at 9 K. Dashed line: raw ${\sigma }_{2c}(\omega )$ data. Solid line: ${\sigma }_{2c}(\omega )$ after the correction for a finite regular contribution characterizing the screening effects that are not related to superconducting carriers. Inset: the $c$-axis superfluid density ${\rho }_{s,c}(\omega )=4\pi \omega {\sigma }_{2c}(\omega )$.