Evidence of a universal and isotropic $2\Delta /k_B{T}_C$ ratio in 122-type iron pnictide superconductors over a wide doping range

We have systematically investigated the doping and the directional dependence of the gap structure in the 122-type iron pnictide superconductors by point contact Andreev reflection spectroscopy. The studies were performed on single crystals of ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$ ($x=0.29$, 0.49, and 0.77) and ${\text{SrFe}}_{1.74}{\text{Co}}_{0.26}{\text{As}}_2$ with a sharp tip of Pb or Au pressed along the $c$-axis or the $ab$-plane direction. The conductance spectra obtained on highly transparent contacts clearly show evidence of a robust superconducting gap. The normalized curves can be well described by the Blonder-Tinkham-Klapwijk model with a lifetime broadening. The determined gap value scales very well with the transition temperature, giving the $2\Delta /k_B{T}_C$ value of $\sim 3.1$. The results suggest the presence of a universal coupling behavior in this class of iron pnictides over a broad doping range and independent of the sign of the doping. Moreover, conductance spectra obtained on $c$-axis junctions and $ab$-plane junctions indicate that the observed gap is isotropic in these superconductors.

Figure 1

(Color online) (a) A typical Josephson $I\text{−}V$ characteristic at 4.2 K obtained on a $c$-axis $\text{Pb}/{\text{Ba}}_{0.23}{\text{K}}_{0.77}{\text{Fe}}_2{\text{As}}_2$ junction and (b) normalized conductance spectrum (circles) obtained on the same junction at 8 K with a modified BTK fit (line).

Figure 2

(Color online) Differential resistance/conductance spectra and analyses obtained on [(a), (c), and (e)] a $c$-axis $\text{Pb}/{\text{Ba}}_{0.51}{\text{K}}_{0.49}{\text{Fe}}_2{\text{As}}_2$ junction and on [(b), (d), and (f)] a $c$-axis $\text{Au}/{\text{Ba}}_{0.71}{\text{K}}_{0.29}{\text{Fe}}_2{\text{As}}_2$ junction. (a) and (b) show examples of spectrum normalization as described in the text. (c) and (d) are temperature dependences of the normalized resistance spectra (circles) with BTK fits (lines). Data are vertically shifted for clarity except the bottom ones. (e) and (f) show the temperature dependence of $Z$ and $\gamma$ used in the fittings. Arrows in (c) indicate small features as discussed in the text.

Figure 3

(Color online) (a) Temperature dependence of the superconductor gap obtained on four representative junctions. Both gap value and temperature scales are reduced for each junction/crystal; the dashed line represents the BCS theory; (b) all low-temperature gap values obtained from our $c$-axis junctions are plotted as a function of the $T_C$. Solid symbols correspond to K-doped single crystals while empty symbols correspond to Co-doped samples. The solid line indicates a constant $2\Delta /k_B{T}_C$ ratio of $\sim 3.1$.

Figure 4

(Color online) Normalized conductance spectra (circles) at 4.2 K obtained on (a) a $c$-axis $\text{Pb}/{\text{SrFe}}_{1.74}{\text{Co}}_{0.26}{\text{As}}_2$ junction and (b) an in-plane $\text{Au}/{\text{SrFe}}_{1.74}{\text{Co}}_{0.26}{\text{As}}_2$ junction. Lines are fits to the data.