Doping-dependent anisotropic superconducting gap in Na${}_{1-\delta }$(Fe${}_{1-x}$Co${}_x$)As from London penetration depth

The London penetration depth was measured in single crystals of self-doped Na${}_{1-\delta }$FeAs (from under doping to optimal doping, $T_c$ from 14 to 27 K) and electron-doped Na(Fe${}_{1-x}$Co${}_x$)As with $x$ ranging from undoped, $x=0$, to overdoped, $x=0.1$. In all samples, the low-temperature variation of the penetration depth exhibits a power-law dependence, $\Delta \lambda \left(T\right)=A{T}^n$, with the exponent that varies in a domelike fashion from $n\sim 1.1$ in the underdoped, reaching a maximum of $n\sim 1.9$ in the optimally doped, and decreasing again to $n\sim 1.3$ on the overdoped side. While the anisotropy of the gap structure follows a universal domelike evolution, the exponent at optimal doping, $n\sim 1.9$, is lower than in other charge-doped Fe-based superconductors (FeSCs). The full-temperature range superfluid density, ${\rho }_s\left(T\right)={\left[\lambda \left(0\right)/\lambda \left(T\right)\right]}^2$, at optimal doping is also distinctly different from other charge-doped FeSCs but is similar to isovalently substituted BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$, believed to be a nodal pnictide at optimal doping. These results suggest that the superconducting gap in Na(Fe${}_{1-x}$Co${}_x$)As is highly anisotropic even at optimal doping.

Figure 1

Low-temperature part of $\Delta \lambda (T/T_c)$ in two Na${}_{1-\delta }$FeAs samples (A and B) in pristine and ultrasonic treated (1-h) states. Dashed lines are representative power-law fits up to $T/T_c=0.1$ for a quantitative analysis. The inset shows a full-temperature range variation of $\Delta \lambda \left(T\right)$ for the same samples.

Figure 2

(a) Low-temperature part of $\Delta \lambda (T/T_c)$ in Na(Fe${}_{1-x}$Co${}_x$)As for $x=0.02$, 0.025, 0.05, 0.08, and 0.10. Dashed lines are representative power-law fits up to $T/T_c=0.2$ for a quantitative analysis. Fitting results are summarized in Fig. 3. The inset shows a full-temperature range variation of $\Delta \lambda \left(T\right)$ for the same samples.

Figure 3

Phase diagram of NaFeAs system. (a) Superconducting “dome” $T_c\left(x\right)$, (b) power-law exponent $n\left(x\right)$, and (c) prefactor $A\left(x\right)$. The results of self-doping study were placed against sonication time (top axis) and scaled by their $T_c$ (see text). Circles show the data for Co-doped samples. Other symbols show the data for self-doped samples.

Figure 4

Experimental normalized superfluid densities ${\rho }_s\left(T\right)$ of optimally doped FeSCs. The top four curves for LiFeAs (Ref. 17), BaCo122 (Ref. 5), BaK122 (Ref. 13), and Ca10-3-8 (Ref. 19) were offset for clarity. Red solid curves show the best fits to an isotropic $s$-wave two-gap $\gamma$ model (Ref. 44), demonstrating good agreement with the data. In clear contrast, the ${\rho }_s$ for optimally doped NaFe${}_{0.975}$Co${}_{0.025}$As (green open squares) and NaFe${}_{0.95}$Co${}_{0.05}$As (blue open circles) cannot be fitted with this fully gapped model, especially at the lowest temperatures, zoomed in at in the inset. For comparison, we also show the data for optimally doped BaP122 ($x=0.33$, black solid dots) (Ref. 20) as well as single $d$ and $s$ gaps (dashed lines) in both clean and dirty limits.