Enhancement of electron correlation due to the molecular dimerization in organic superconductors $\beta -\left(\mathrm{BDA-TTP}{)}_{2}X\right(X={\mathrm{I}}_3, {\mathrm{SbF}}_6)$

We perform a first-principles band calculation for quasi-two-dimensional organic superconductors $\beta -(\mathrm{BDA}-{\mathrm{TTP})}_2{\mathrm{I}}_3$ and $\beta -(\mathrm{BDA}-{\mathrm{TTP})}_2{\mathrm{SbF}}_6$. The first-principles band structures between the ${\mathrm{I}}_3$ and ${\mathrm{SbF}}_6$ salts are apparently different. We construct a tight-binding model for each material which accurately reproduces the first-principles band structure. The obtained transfer energies give the differences as follows: (i) larger dimerization in the ${\mathrm{I}}_3$ salt than the ${\mathrm{SbF}}_6$ salt, and (ii) different signs and directions of the interstacking transfer energies. To decompose the origin of the difference into the dimerization and the interstacking transfer energies, we adopt a simplified model by eliminating the dimerization effect and focus only on the difference caused by the interstacking transfer energies. From the analysis using the simplified model, we find that the difference of the band structure comes mainly from the strength of the dimerization. To compare the strength of the electron correlation having roots in the band structure, we calculate the physical properties originating from the effect of the electron correlation such as the spin susceptibility applying the two-particle self-consistent method. We find that the maximum value of the spin susceptibility for the ${\mathrm{I}}_3$ salt is larger than that of the ${\mathrm{SbF}}_6$ salt. Hypothetically decreasing the dimerization within the model of the ${\mathrm{I}}_3$ salt, the spin susceptibility takes almost the same value as that of the ${\mathrm{SbF}}_6$ salt for the same magnitude of the dimerization. We expect that the different ground state between the ${\mathrm{I}}_3$ and ${\mathrm{SbF}}_6$ salt mainly comes from the strength of the dimerization which is apparently masked in the band calculation along a particular $k$ path.

Figure 1

Crystal structure of the ${\mathrm{I}}_3$ salt from (a) the side view and (b) the conductive layer of the BDA-TTP molecules.

Figure 2

(a) Calculated first-principles band structure and (b) Fermi surface for the ${\mathrm{I}}_3$ salt; (c) first-principles band structure and (d) Fermi surface for the ${\mathrm{SbF}}_6$ salt. In both figures of the band structures, the red curves represent the first-principles band structures and the blue solid curves give the tight-binding fit.

Figure 3

Tight-binding model for $\beta$-(BDA-${\mathrm{TTP})}_{2}X$, where left (right) part shows the first (second) nearest neighbor transfer energies. Solid ellipses represent the BDA-TTP molecules and the dashed rectangle is the unit cell.

Figure 4

The lattice structures of (a) the ${\mathrm{I}}_3$ and (b) the ${\mathrm{SbF}}_6$ salt. Blue solid lines represent the tilting angles of the donor molecules, which is measured from the $c$ direction taken in the horizontal direction. In the lower panel, the ellipses represent the donor molecules, the black solid lines show the intrastacking transfer, and the red solid (black dotted) lines represent the main (not main) interstacking transfer.

Figure 5

The simplified model for (a) the ${\mathrm{I}}_3$ salt and (b) the ${\mathrm{SbF}}_6$ salt, where the linewidth schematically represents the magnitude of the transfer energies, and the solid (dashed) lines represent the negative (positive) value of the transfer energies. (c) The band structures measured from the Fermi energy and an inset shows the Fermi surfaces of the simplified model by eliminating the dimerization for the two salts, where the red solid (blue dashed) curves represent the results of the ${\mathrm{I}}_3$ (${\mathrm{SbF}}_6$) salt.

Figure 6

Temperature dependence of (a) $U_{\mathrm{sp}}$ and $U_{\mathrm{SDW}}$ for the left scale and $U_{\mathrm{SDW}}/U_{\mathrm{sp}}$ for the right scale, (b) $U_{\mathrm{ch}}$, (c) the double occupancy $〈D〉$, and (d) the inverse of the maximum value of the diagonalized spin susceptibility for the left scale and $U_{\mathrm{sp}}{\chi }_0$ for the right scale in the model of the ${\mathrm{I}}_3$ salt. Blue dashed lines represent the line extrapolating each value and the black dotted lines are about $T=0.0038\mathrm{eV}$.

Figure 7

(a) The absolute value of the Green's function and (b) the diagonalized spin susceptibility for the model of the ${\mathrm{I}}_3$ salt at $T=0.004\mathrm{eV}$, where the arrow represents the nesting vector.

Figure 8

The strength of the dimerization $t_{p2}/t_{p1}$ dependence of (a) $U_{\mathrm{sp}}$ and $U_{\mathrm{SDW}}$, (b) $U_{\mathrm{ch}}$, (c) the double occupancy $〈D〉$, and (d) the maximum value of the diagonalized spin susceptibility for the model of the ${\mathrm{I}}_3$ salt with $U=0.8\mathrm{eV}$ and $T=0.004\mathrm{eV}$. The results obtained for the model of the ${\mathrm{SbF}}_6$ salt with the same $U$ and $T$ are also shown by the diamonds (indicated by the arrows) at the value of $t_{p2}/t_{p1}$ of the ${\mathrm{SbF}}_6$ salt, and in (a), the solid blue (open purple) diamonds correspond to $U_{\mathrm{sp}}$ ($U_{\mathrm{SDW}}$).