Thermal-transport measurement of the nodal superconductor KFe$_2$As$_2$

Hole-doped Fe-based superconductors, (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$, possess two different superconducting gap structures; a fully-gapped state near the optimally dope (x$\sim$0.5) and a nodal gap state at the hole-dope end (x = 1). To investigate the detail gap structure, we performed thermal-transport measurements of KFe$_2$As$_2$ with very high purity (RRR$\sim$ 1,600) down to 80 mK. From the temperature dependence of thermal conductivity at zero field, we find a finite residual of $\kappa / T$ in the zero-temperature limit. This residual increases by magnetic field as $\propto \sqrt{H}$ in low fields, followed by a rapid increase near $H_{c2}$. Thermal conductivity measurements of different dopes (x = 0.88, 0.93) will be reported.