Evaluating model parameters of the $\kappa$- and ${\beta }^{\prime }$-type Mott insulating organic solids

We elucidate the model parameters for a series of organic crystals called $\kappa$- and ${\beta }^{\prime }$-type salts by constructing the maximally localized Wannier orbitals which reproduce the bulk energy band of the first-principles methods based on the density functional theory (DFT). These materials host a dimer Mott insulator, localizing one hole per dimerized ET molecules due to strong on-dimer interaction, $U_{\mathrm{d}}$. For all these materials, we evaluate the parameters of the two representative effective lattice models in units of molecule and on dimer, and clarify two issues. First, the conventional relationships between the two models called “dimer approximation” does not hold. Second, contrary to the previous semiempirical estimates, the degree of dimerization (which approximates $U_{\mathrm{d}}$) does not depend much on materials, and that the overall ground state properties are controlled by the degree of anisotropy of the triangular lattice, denoted as $|t_c/t_a|$ in units of dimers. We update the DFT estimates $|t_c/t_a|$ of $\kappa$-ET${}_2$Cu${}_2$(CN)${}_3$, showing that it falls on a class of regular triangle with the strongest degree of frustration.

Figure 1

(a),(b) Simplified dimer-based anisotropic triangular lattice of $\kappa$- and ${\beta }^{\prime }$-ET${}_{2}X$. $t_{\mu \nu }=t_a\sim t_d$ are the interdimer transfer integrals in Eq. (1). (c),(d) Molecular arrangements of the two-dimensional conducting layer of $\kappa$- and ${\beta }^{\prime }$-ET${}_{2}X$. The dominant transfer integrals, $t_{ij}=t_1\sim t_5$, of Eq. (2) are shown. (e) Scheme of DFT. The comparison of the two set of transfer integrals show that the dimer approximation does not hold.

Figure 2

DFT band structures of $\kappa$-ET₂Cu₂(CN)₃ based on two different crystal data: (a) Geiser et al.[24] and (b) Schlueter et al.[19] There are two possible orientations of the CN${}^{-1}$ group with the symmetry of $P{2}_1$ (red lines) and $P_c$ (green lines), respectively. However, both symmetries using $t_1,t_2,t_3$, and $t_4$ give almost the same tight-binding band structures shown in blue broken two lines put together (but are not distinguishable).

Figure 3

DFT band structures of (a) $\kappa$-NCS, (b) $\kappa$-d${}_8$-Cl (deutrated), and (c) ${\beta }^{\prime }$-ICl${}_2$. The tight-binding band structure using $t_1\sim t_4$ is shown together in broken lines. The crystal structures along the two-dimensional ET conducting plane are given on the right panel, where only the TTF structures of the ET molecules are shown for simplicity.