Insulating Vortex Core near QCP in CeCoIn$_5$*

We have investigated the vortex core of the superclean unconventional heavy fermion superconductor CeCoIn$_5$ by studying the flux flow dissipation in the mixed state for two magnetic field orientations, i.e., $H \parallel c$ axis and $H \parallel ab $ plane, at temperatures down to 1.8 K. The vortex core in the mixed state of CeCoIn$_5$ is insulator-like, in contrast to the metallic behavior of CeCoIn$_5$ in its normal state, at temperatures $T$ larger than the supercondcting transition temperature $T_c$. Moreover, the abnormal insulating behavior of the vortex core is strongly suppressed when CeCoIn$_5$ is tuned away from the quantum critical point (QCP) by applying pressure. This latter result gives firm evidence that quantum criticality plays an important role in the interaction between superconductivity and magnetism, hence is responsible for the emergence of unconventional superconductivity. A scaling law of the flux flow resistivity has also been found and will be discussed.