Multi-gap nodeless superconductivity in iron selenide FeSe$_x$: evident from quasiparticle heat transport

The in-plane thermal conductivity $kappa$ of the iron selenide superconductor FeSe$_x$ ($T_c$ = 8.8 K) were measured down to 120 mK and up to 14.5 T ($simeq 3/4 H_{c2}$). In zero field, the residual linear term $kappa_0/T$ at $ T to 0$ is only about 16 $mu$W K$^{-2}$ cm$^{-1}$, less than 4% of its normal state value. Such a small $kappa_0/T$ does not support the existence of nodes in the superconducting gap. More importantly, the field dependence of $kappa_0/T$ in FeSe$_x$ is very similar to that in NbSe$_2$, a typical multi-gap s-wave superconductor. We consider our data as strong evidence for multi-gap nodeless superconductivity in FeSe$_x$. This kind of superconducting gap structure may be generic for all Fe-based superconductors.