Specific-Heat Measurements of the Gap Structure of the Organic Superconductors $\kappa \mathrm{\text{−}}(\mathrm{ET}{)}_2\mathrm{Cu}[\mathrm{N}(\mathrm{CN}{)}_2]\mathrm{Br}$ and $\kappa \mathrm{\text{−}}(\mathrm{ET}{)}_2\mathrm{Cu}(\mathrm{NCS}{)}_2$

We present high resolution heat capacity measurements of the organic superconductors $\kappa \mathrm{\text{−}}(\mathrm{ET}{)}_2\mathrm{Cu}[\mathrm{N}(\mathrm{CN}{)}_2]\mathrm{Br}$ and $\kappa \mathrm{\text{−}}(\mathrm{ET}{)}_2\mathrm{Cu}(\mathrm{NCS}{)}_2$ in fields up to 14 T. We use the high field data to determine the normal state specific heat and hence extract the behavior of the electronic specific heat $C_{\mathrm{el}}$ in the superconducting state in zero and finite fields. We find that in both materials for $T/T_c\lesssim 0.3$, $C_{\mathrm{el}}(H=0)\sim T^2$ indicating $d$-wave superconductivity. The data are well described by a strong coupling $d$-wave model from our base temperature ($T/T_c\sim 0.1$) right up to $T_c$. Our data help to resolve the controversy regarding the order parameter symmetry in these materials.

Figure 1

Left: Zero field specific-heat data for $\kappa \mathrm{\text{−}}\mathrm{Br}$ and $\kappa \mathrm{\text{−}}\mathrm{NCS}$. Upper right-hand panel: $C/T$ vs $T^2$ for both compounds in fields of 0 and 14 T. The upper curve for each field is $\kappa \mathrm{\text{−}}\mathrm{NCS}$. Lower right-hand panel: Field dependence of $\gamma$ for both compounds.

Figure 2

Top: $\Delta C=C(0)-C(14\mathrm{T})$ vs $T$ for $\kappa \mathrm{\text{−}}\mathrm{Br}$, along with several fits. The thin solid line is a fit to the strong coupling $d$-wave model, whereas the thick solid line is the same fit convoluted with a Gaussian. Similarly, the dashed lines are fits to the strong coupling $s$-wave model. Bottom: Enlarged view of the low temperature part of the upper panel (the convoluted fits are indistinguishable and are omitted for clarity).

Figure 3

The same plots as Fig. 2 but for $\kappa \mathrm{\text{−}}\mathrm{NCS}$.

Figure 4

$\Delta C/T$ vs ($T/T_c$) for $\kappa \mathrm{\text{−}}\mathrm{Br}$ and $\kappa \mathrm{\text{−}}\mathrm{NCS}$. The solid lines are fits to the $d$-wave model and the dashed and dotted lines are the $s$-wave fits for each compound, respectively.