Mixed pairing symmetry in $\kappa$-(BEDT-TTF)$_2$X organic superconductors from ultrasonic velocity measurements

Discontinuities in elastic constants are detected at the superconducting transition of layered organic conductors $\kappa$-(BEDT-TTF)$_2$X by longitudinal and transverse ultrasonic velocity measurements. Symmetry arguments show that discontinuities in shear elastic constants can be explained in the orthorhombic compound only if the superconducting order parameter has a mixed character that can be of two types, either A$_{1g}$+B$_{1g}$ or B$_{2g}$+B$_{3g}$ in the classification of irreducible representations of the orthorhombic point group D$_{2h}$. Consistency with other measurements suggests that the A$_{1g}$+B$_{1g}$ d$_{xy}$+d$_{z(x+y)}$) possibility is realized. Such clear symmetry-imposed signatures of mixed order parameters have not been observed in other superconducting compounds.