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

The London penetration depth was measured in single crystals of self-doped Na$_{1-\delta}$FeAs (from under - 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, $\Delta \lambda (T) = AT^n$, with the exponent that varies in a dome - like 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 universal dome-like evolution, the exponent at the optimal doping, $n \sim 1.9$, is lower than in other charge - doped Fe-based superconductors (FeSCs). The full - temperature range superfluid density, $\rho_s(T) = (\lambda(0)/\lambda(T))^2$, at the 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 the optimal doping. These results suggest that the superconducting gap in Na(Fe$_{1-x}$Co$_{x}$)As is highly anisotropic even at the optimal doping.