Low temperature thermal conductivity of single crystal Ba$_{1-x}$K$_x$Fe$_2$As$_2$

Novel iron-arsenic based superconductors with T$_c$ $>$ 50 K form a good reference for studying physical processes, underlyning high-T$_c$ superconductivity. Indeed, the importance of unique features of the superconductivity in cuprates, like proximity to Mott insulating state in the phase diagram, magnetism, d-wave superconducting pairing can be tested experimentally. Here we report a study aiming at understanding the symmetry of the superconducting gap in iron-arsenic compounds. Temperature and magnetic field dependence of low temperature thermal conductivity of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ single crystals was studied down to 60 mK (T$_c$/500) and in magnetic fields up to 15 T (H/H$_{c2}\cong$~ 0.25 ). We find no residual linear term in zero magnetic field and can therefore exclude a superconducting gap with a line of nodes.