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

Abstract

The London penetration depth, $\hat{I}»$, is directly related to the density, $n_s$, of the Cooper pairs ($\hat{I}{»}^2\propto 1/n_s$) 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 ($\hat{I}{»}_{ab}$) and out-of-plane ($\hat{I}{»}_c$) penetration depths in single crystals of electron-doped Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$. As is the case for other pnictides, $\hat{I}»(T)\sim T^n$ 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 $\hat{I}{»}_c(T)$ 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.