Evolution of Superconducting H$_{c2}$ Transition with La-Doping in Ce$_{1-x}$La$_x$CoIn$_5$

Recent measurements of the heavy-fermion superconductor CeCoIn$_5$ have revealed a field-tuned quantum critical point which coincides with a {\it first-order} superconducting transition H$_{c2}$ as $T \to 0$ [1], resulting in a completely unique and intriguing H-T phase diagram with no known magnetic phase. By substituting La for Ce, a gradual destruction of the superconducting phase allows an investigation of the correlation between the order of H$_{c2}$ and the field-tuned quantum critical behaviour. Here we report low temperature heat and charge transport measurements of Ce$_{1-x}$La$_x$CoIn$_5$ as a function of field and doping, revealing an intriguing evolution of the quantum critical behaviour in this system. \newline \newline [1] J. Paglione {\it et al.}, Phys. Rev. Lett. 91, 246405 (2003).