Thermal conductivity of overdoped BaFe$_{1.73}$Co$_{0.27}$As$_2$ single crystal: Evidence for nodeless multiple superconducting gaps and interband interactions

The in-plane thermal conductivity $kappa$ of overdoped FeAs-based superconductor BaFe$_{1.73}$Co$_{0.27}$As$_2$ ($T_c$ = 8.1 K) single crystal was measured down to 80 mK. In zero field, the residual linear term $kappa_0/T$ is negligible, suggesting a nodeless superconducting gap in the $ab$-plane. In magnetic field, $kappa_0/T$ increases rapidly, very different from that of conventional s-wave superconductors. This anomalous $kappa_0/T(H)$ may reveal an exotic superconducting gap structure in overdoped BaFe$_{1.73}$Co$_{0.27}$As$_2$: the vanishing hole ($beta$) pocket has a much larger gap than the electron ($gamma$ and $delta$) pockets which contain most of the carriers. Such an exotic gap structure is an evidence for superconducting state induced by interband interactions, in which the band with the {it smaller} density of states has a {it larger} gap.