Lattice vibrations of the charge-transfer salt $kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_{3}$: novel interpretation of the electrodynamic response in a spin-liquid compound

The dimer Mott insulator $kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ exhibits unusual electrodynamic properties. Numerical investigations of the electronic ground state and the molecular and lattice vibrations reveal the importance of the Cu$_2$(CN)$_3^-$ anion network coupled to the BEDT-TTF molecules: The threefold cyanide coordination of copper and linkage isomerism in the anion structure cause a loss of symmetry, frustration, disorder, and domain formation. Our findings consistently explain the temperature and polarization-dependent THz and infrared measurements, reinforce the understanding of dielectric properties and have important implications for the quantum spin-liquid state, which should be treated beyond two-dimensional, purely electronic models.