Magnetic-field-angle-resolved heat capacity of dimer-Mott organic superconductors $\kappa \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}X$ is reported (BEDT-TTF and $X$ represent bis(ethylenedithio)tetrathiafulvalene and a monovalent anion, respectively). Temperature and field dependence of heat capacity indicates that the superconductivity has line nodes on the Fermi surface, which is a typical feature of $d$-wave superconductivity. In-plane field-angle dependence exhibits fourfold oscillations as well as twofold oscillations due to anisotropy of superconducting gap functions. From analyses of the fourfold term, the gap symmetry is determined as $d_{x^2-y^2}+s_{\pm }$ for $X=\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]\mathrm{Br}$ and $d_{xy}$ for $X=\mathrm{Ag}{\left(\mathrm{CN}\right)}_2{\mathrm{H}}_2\mathrm{O}$. We suggest that the symmetry difference comes from the competition of $d_{xy}$ and $d_{x^2-y^2}$ antiferromagnetic fluctuations depending on lattice geometry.

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• Superconducting order parameter
• Superconductivity
• Organic superconductors
• Specific heat measurements