Thermal conductivity of strong coupling V$_{1-x}$Ti$_x$ superconductors in the Mott-Ioffe-Regel limit

Abstract

We report an enhancement of thermal conductivity ($\kappa$) below the superconducting transition temperature ($T_C$) in the high carrier density $\beta$-V$_{1-x}$Ti$_x$ alloys. We find that the point defects generated when Ti is added to V reduce the electron mean free path down to the inter-atomic distances and make the high frequency phonons ineffective in carrying heat. In this Mott-Ioffe-Regel limit, the phonon thermal conductivity is dominated by the low frequency phonons limited by the scattering due to the electrons. The formation of Cooper pairs below the $T_C$ re-normalizes the phonon mean free path and enhances the $\kappa$.