Probing the Superconducting Energy Gap from Infrared Spectroscopy on a ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ Single Crystal with $T_c=37\mathrm{K}$

We performed optical spectroscopy measurement on a superconducting ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ single crystal with $T_c=37\mathrm{K}$. Formation of the superconducting energy gaps in the far-infrared reflectance spectra below $T_c$ is clearly observed. A flat and close to unity reflectance is observed roughly below $150{\mathrm{cm}}^{-1}$ for $T\ll T_c$, following an $s$-wave pairing line shape. A more rapid decrease occurs near $200{\mathrm{cm}}^{-1}$, leading to a peak in the ratio of the reflectance at $T\ll T_c$ over that for $T\ge T_c$. We determined the absolute value of the penetration depth at 10 K as $\lambda \simeq 2000\pm 80\AA$. A spectral weight analysis shows that the Ferrell-Glover-Tinkham sum rule is satisfied at low energy scale, less than $6\Delta$.

Figure 1

The dc resistivity as a function of temperature for a ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ single crystal. Inset shows the ac susceptibility of the sample. Sharp superconducting transition occurs at $T_c=37\mathrm{K}$.

Figure 2

$T$-dependent $R(\omega )$ curves in the far-infrared region. The inset shows $R(\omega )$ over broad frequencies up to $25000{\mathrm{cm}}^{-1}$.

Figure 3

$T$-dependent ${\sigma }_1(\omega )$ curves. The inset shows ${\sigma }_1(\omega )$ at 10 and 45 K. The shaded area represents the missing area due to the opening of superconducting energy gap.

Figure 4

The reflectance $R(\omega )$ at 10 K normalized to the values at 45 K in the normal state. A peak near $200{\mathrm{cm}}^{-1}$ is seen.

Figure 5

Frequency dependent London penetration depth $\lambda (\omega )=c/{\omega }_{ps}=c/\sqrt{4\pi \omega {\sigma }_2(\omega )}$ for ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ at 10 K.