Revision of Model Parameters for $\kappa$-Type Charge Transfer Salts: An Ab Initio Study

Intense experimental and theoretical studies have demonstrated that the anisotropic triangular lattice as realized in the $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_{2}X$ family of organic charge transfer salts yields a complex phase diagram with magnetic, superconducting, Mott insulating, and even spin liquid phases. With extensive density functional theory calculations we refresh the link between many body theory and experiment by determining hopping parameters of the underlying Hubbard model. This leads us to revise the widely used semiempirical parameters in the direction of less frustrated, more anisotropic triangular lattices. The implications of these results on the systems’ description are discussed.

Figure 1

Structure of $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2{\mathrm{Cu}}_2(\mathrm{CN}{)}_3$ as typical example of the $\kappa$-type CT salts. (a) Side view with ET layers separated by insulating ${\mathrm{Cu}}_2(\mathrm{CN}{)}_3$ anion layers. (b) ET lattice, viewed in the $bc$ plane. The unit cell containing four ET molecules is shown. (c) ET lattice shown in the same projection as (b) where the ET molecules have been replaced by single spheres. ET dimers are emphasized by heavier bonds. (d) Lattice of ET dimers, replaced by single spheres.

Figure 2

DFT band structures of (a) $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2{\mathrm{Cu}}_2(\mathrm{CN}{)}_3$ at ambient pressure and at $P=0.75\mathrm{GPa}$, and of (b) $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2\mathrm{Cu}[\mathrm{N}(\mathrm{CN}{)}_2]\mathrm{Cl}$ shown with symbols. Lines represent the tight-binding fits to the bands close to $E_{\mathrm{F}}$ deriving from ET molecules.

Figure 3

Fermi surface cuts for nonmagnetic $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2{\mathrm{Cu}}_2(\mathrm{CN}{)}_3$ at ambient pressure (black) and at $P=0.75\mathrm{GPa}$ (light). Thin lines show the respective first Brillouin zone. The combined elliptical orbit as detected by AMRO measurements (see text) is indicated by broken lines.

Figure 4

Overview of hopping parameters obtained from GGA (filled symbols) and LDA (open symbols) calculations for $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2{\mathrm{Cu}}_2(\mathrm{CN}{)}_3$, $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2\mathrm{Cu}(\mathrm{SCN}{)}_2$, and $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2\mathrm{Cu}[\mathrm{N}(\mathrm{CN}{)}_2]\mathrm{Cl}$. The spread of $t$ and $t^{\prime }$ parameters depending on basis set, functional, and number of fitted bands yields $t^{\prime }/t$ ratios with a margin of error indicated by lines and shaded regions. Arrows indicate the change of $t^{\prime }/t$ ratio due to application of a pressure of $P=0.75\mathrm{GPa}$.