Thermal conductivity of the iron-based superconductor FeSe : Nodeless gap with strong two-band character

The thermal conductivity $\kappa$ of the iron-based superconductor FeSe was measured at temperatures down to 50~mK in magnetic fields up to 17~T. In zero magnetic field, the residual linear term in the $T=0$ limit, $\kappa_0/T$, is vanishingly small. Application of a magnetic field $H$ causes no increase in $\kappa_0/T$ initially. Those two facts show that there are no zero-energy quasiparticles that carry heat and therefore no nodes in the superconducting gap of FeSe. The full field dependence of $\kappa_0/T$ has the classic shape of a two-band superconductor, such as MgB$_2$. It rises initially with a characteristic field $H^{\star} \simeq H_{\rm c2} / 25$, and then more slowly up to $H_{\rm c2} = 14$~T. We interpret this in terms of a small gap $\Delta_{\rm A} \simeq \Delta_0 / 5$ on some part of the Fermi surface, with a large gap $\Delta_{\rm B} = \Delta_0$ in the region that controls $H_{\rm c2}$.