Three-dimensional nodal superconducting gap in single crystals Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$

The London penetration depth, $\lambda$, is directly related to the density, $n_{s}$, of the Cooper pairs ($\lambda^{2}\propto 1/n_{s}$) and its variation with temperature provides valuable insight into the pairing mechanism. Here we study the evolution with doping of the temperature dependence of the in-plane ($\lambda_{ab}$) and out-of-plane ($\lambda_{c}$) penetration depths in single crystals of electron-doped Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$. As is the case for other pnictides, $\lambda(T) \sim T^n$ over the whole doping range and this behavior extends down to at least $T=T_c/100$, setting a very small upper limit on the gap minimum. Furthermore, in the overdoped regime: 1) the exponent $n$ becomes substantially smaller than 2, which is incompatible with the models that explain power-law behavior to be due to scattering; 2) the exponent $n$ becomes anisotropic, with $\lambda_{c}(T)$ showing a clear $T$-linear behavior over a large temperature interval. These findings suggest that in the overdoped regime the superconducting gap in iron-based pnictide superconductors develops nodal structure, which unlike in the cuprates, cannot be understood within a two-dimensional picture.