  The newly discovered superconductivity in MgCNi3, though with Tc<8 K lower
than that of the celebrated MgB2, is probably even more interesting in its many
puzzling physical properties. MgCNi3 has been theoretically speculated to be
unstable towards ferromagnetism. However, there are numerous evidences from the
specific heat C(T), Tunneling spectroscopy and NMR experiments indicating
conventional s-wave superconductivity in MgCNi3. The Hall effect and the
thermoelectric power experiments suggest that the carriers responsible for the
transport properties are electrons, in obvious contrast to holes predicated by
the band structure calculations. In this article, we report the results of C(T)
experiments, upper critical field Hc2 measurements, and the pressure effects on
MgCNi3. These experimental evidences clearly demonstrate that superconductivity
in MgCNi3 is well explained within the conventional electron-phonon interaction
scenario, at most with minor modifications from the magnetic interaction. The
thermodynamic data C(T) is consistent with the conventional s-wave order
parameter. Hc2 of all samples follows a universal WHH relation . Surprisingly,
dTc/dP is positive which leaves room for further improvements in band structure
calculations. There are other serious discrepancies between experiments and
theory like in the transport properties and x-ray photoemission. The possible
reconciliation within the two-band model and the consequent difficulties are
discussed.
