London penetration depth in heavily over-doped Ba(Fe$_{1-x}$Co$_x$)$_{2}$As$_{2}$

The low-temperature variation of London penetration depth, $\Delta\lambda(T)$, has been previously studied in heavily over-doped Ba(Fe$_{1-x}$Ni$_{x}$)$_{2}$As$_{2}$ [1] and the authors suggested the development of line nodes. Similar conclusion was made from thermal conductivity measurements in Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ [2]. However, $\Delta\lambda(T)$ in this system has only been measured for $x \leq x=0.102$ [3], which is not far enough from optimal doping. Here we report tunnel - diode resonator (TDR) measurements in heavily overdoped single crystals of Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ with Co content of $x=0.108$ ($T_{c}$=14.8~K) and $x=0.127$ ($T_{c}$=9~K. We found a robust power-law behavior of $\Delta \lambda = A T^n$ with $n=2.5$ and $n=2.11$ respectively. To test whether the nodes are symmetry imposed or accidental, samples were irradiated with heavy ions. The produced disorder, leads to a decrease in $T_c$ and of the exponent $n$. These results effects will be discussed in a context of unconventional pairing in Fe-based superconductors. \\[4pt] [1] C. Martin {\it et. al.}, Phys. Rev. B {\bf 81}, 060505 (2010).\\[0pt] [2] J.-Ph. Reid {\it et. al.}, Phys. Rev. B {\bf 82}, 064501 (2010).\\ [0pt] [3] R.T. Gordon et.al. Phys. Rev. B {\bf 82}, 054507 (2010).