Evidence for strong electron-phonon coupling in MgCNi_3
  The title compound is investigated by specific heat measurements in the normal and superconducting state supplemented by upper critical field transport, susceptibility and magnetization measurements. From a detailed analysis including also full potential electronic structure calculations for the Fermi surface sheets, Fermi velocities and partial densities of states the presence of both strong electron-phonon interactions and considerable pair-breaking has been revealed. The specific heat and the upper critical field data can be described to first approximation by an effective single band model close to the clean limit derived from a strongly coupled predominant hole subsystem with small Fermi velocities. However, in order to account also for Hall-conductivity and thermopower data in the literature, an effective general two-band model is proposed. This two-band model provides a flexible enough frame to describe consistently all available data within a scenario of phonon mediated s-wave superconductivity somewhat suppressed by sizeable electron-paramagnon or electron-electron Coulomb interaction. For quantitative details the relevance of soft phonons and of a van Hove type singularity in the electronic density of states near the Fermi energy is suggested. 
A. Waelte, G. Fuchs, K.-H. Mueller, A. Handstein, K. Nenkov, V. N.   Narozhnyi, S.-L. Drechsler, S. Shulga, H. Rosner and L....