Thermal conductivity study of KFe$_2$As$_2$ single crystal: clear evidence for unconventional superconducting gap with nodes

The in-plane resistivity $\rho$ and thermal conductivity $\kappa$ of extremely overdoped KFe$_2$As$_2$ ($T_c$ = 3.0 K) single crystal were studied. It is found that $\rho \sim T^{1.5}$ at low temperature, a typical non-Fermi liquid behavior of electrons scattered by antiferromagnetic spin fluctuations. In zero field, we observed a large residual linear term $\kappa_0/T$, about one third of the normal-state value. In low magnetic fields, $\kappa_0/T(H)$ increases very fast. Such a behavior of $\kappa_0/T$ mimics the d-wave cuprate superconductors, therefore provides clear evidence for nodes in the superconducting gap of KFe$_2$As$_2$. Based on the Fermi surface topology of KFe$_2$As$_2$, it is believed that the dominant intraband pairing via antiferromagnetic spin fluctuations results in the unconventional superconducting gap with nodes.