Specific heat study of the effect of cooling rate on the superconducting and normal states of $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br

It is well known that the $T_c$ of $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br is dependent on the rate it is cooled in the temperature range 80-60~K. One interpretation of this effect is that rapid cooling introduces disorder which suppresses $T_c$ because of its unconventional nature. Here we present a specific heat study of this effect in both hydrogenated and deuterated samples. We find that not only does $T_c$ depend on the cooling rate, but that the normal-state Sommerfeld coefficient, $\gamma$, is strongly suppressed (by up to a factor 2) with rapid cooling. The data indicate that rapid cooling induces macroscopic phase separation between an insulating and metallic / superconducting phase at low temperature. The field dependence of $\gamma$ for the deuterated sample is highly unusual. As the field is increased it initially increases in a conventional way then suddenly collapses to a small value. We interpret this as evidence for a field induced superconductor-insulator transition.