Two band gap field-dependent thermal conductivity of $MgB_2$

The thermal conductivity $\kappa (H,T)$ of the new superconductor $MgB_2$ was studied as a function of the temperature and a magnetic field. No anomaly in the thermal conductivity $\kappa (H,T)$ is observed around the superconducting transition in absence or presence of magnetic fields up to 14 Tesla; upon that field the superconductivity of $MgB_2$ persisted. The thermal conductivity in zero-field shows a $T$-linear increase up to 50K. The thermal conductivity is found to increase with increasing field at high fields. We interpret the findings as if there are two subsystems of quasiparticles with different field-dependent characters in a two ($L$ and $S$)-band superconductor reacting differently with the vortex structure. The unusual enhancement of $\kappa (H ,T)$ at low temperature but higher than a ($H_{c2S}\simeq 3T$) critical field is interpreted as a result of the overlap of the low energy states outside the vortex cores in the $S$-band.