Anomalous doping effects of Co impurities on the iron-based superconductor KFe$_2$As$_2$: evidence for a d-wave superconducting state

High-quality K(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystals have been grown by using KAs flux method. Instead of increasing the transition temperature $T_{\rm c}$ through electron doping, we find that Co impurities rapidly suppress the superconductivity, with $T_{\rm c}$ down to zero at only $x \approx$ 0.04. Such an effective suppression of $T_{\rm c}$ by impurities is distinctly different from that observed in Ba$_{0.5}$K$_{0.5}$Fe$_2$As$_2$, but mimics that in d-wave cuprate and heavy-fermion superconductors. Thermal conductivity measurements show the universal heat conduction for $x$ = 0 and 0.034 superconducting samples, namely a constant residual linear term $\kappa_0/T$ in zero field, despite that the scattering rate increases by 70 times. All these evidences support a d-wave superconducting state in KFe$_2$As$_2$.