Thermal conductivity of single crystalline MgB_2
  The ab-plane thermal conductivity $\kappa$ of single-crystalline hexagonal MgB_2 has been measured as a function of magnetic field H with orientations both parallel and perpendicular to the c-axis and at temperatures between 0.5 and 300 K. In the mixed state, $\kappa(H)$ measured at constant temperatures reveals features that are not typical for common type-II superconductors. The observed behavior may be associated with the field-induced reduction of two superconducting energy gaps, significantly different in magnitude. A nonlinear temperature dependence of the electronic thermal conductivity is observed in the field-induced normal state at low temperatures. This behavior is at variance with the Wiedemann-Franz law, and suggests an unexpected instability of the electronic subsystem in the normal state at T ~ 1 K. 
A.V. Sologubenko, J. Jun, S. M. Kazakov, J. Karpinski, H.R. Ott