$d_{x^2-y^2}$- versus $d_{\mathrm{xy}}$- like pairings in organic superconductors $\kappa -(\mathrm{BEDT}-\mathrm{TTF}{)}_{2}X$

Pairing symmetry in $\kappa -(\mathrm{BEDT}-\mathrm{TTF}{)}_{2}X$ is reexamined by applying the fluctuation exchange method to the Hubbard model on the original four-band lattice. Our study is motivated by the discrepancy between recent thermal conductivity/tunneling spectroscopy experiments and the previous theories based on the effective single or two-band model. In contrast to the previous theories, we find that $d_{x^2-y^2}$-like pairing dominates over $d_{\mathrm{xy}}$ in agreement with recent experiments. Our study provides a general lesson that even if the Fermi surface seems to be reproduced by an effective model, the pairing symmetry can be different from that of the original system.