Proximity of the Layered Organic Conductors $\alpha \mathrm{\text{−}}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_{2}M\mathrm{H}\mathrm{g}(\mathrm{S}\mathrm{C}\mathrm{N}{)}_4$ $(M=\mathrm{K},\mathrm{N}{\mathrm{H}}_{\mathrm{4}})$ to a Charge-Ordering Transition

While the optical properties of the superconducting salt $\alpha \mathrm{\text{−}}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2\mathrm{\text{−}}\mathrm{N}{\mathrm{H}}_{\mathrm{4}}\mathrm{H}\mathrm{g}(\mathrm{S}\mathrm{C}\mathrm{N}{)}_4$ remain metallic down to 2 K, in the nonsuperconducting K analog a pseudogap develops at frequencies of about $200{\mathrm{c}\mathrm{m}}^{-1}$ for temperatures $T<200\mathrm{K}$. We show that the optical conductivity calculated with exact-diagonalization techniques on an extended Hubbard model at quarter filling is consistent with the observed low-frequency feature. We argue that the different optical responses observed are a consequence of the proximity of these compounds to a charge-ordering transition driven by the intermolecular Coulomb repulsion.

Figure 1

(a) Frequency dependent reflectivity and (b) optical conductivity of $\alpha \mathrm{\text{−}}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2\mathrm{K}\mathrm{H}\mathrm{g}(\mathrm{S}\mathrm{C}\mathrm{N}{)}_4$ for different temperatures as indicated. The panels (c) and (d) show the reflectivity and conductivity, respectively, of $\alpha \mathrm{\text{−}}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2{\mathrm{N}\mathrm{H}}_4\mathrm{H}\mathrm{g}(\mathrm{S}\mathrm{C}\mathrm{N}{)}_4$. The measurements were performed for $E\parallel c$; the $E\perp c$ reflection data are displayed in the corresponding insets. For both polarization the reflectivity of $(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2\mathrm{K}\mathrm{H}\mathrm{g}(\mathrm{S}\mathrm{C}\mathrm{N}{)}_4$ has a dip at around $200{\mathrm{c}\mathrm{m}}^{-1}$.

Figure 2

Optical conductivity of $\alpha \mathrm{\text{−}}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2\mathrm{K}\mathrm{H}\mathrm{g}(\mathrm{S}\mathrm{C}\mathrm{N}{)}_4$ (solid lines) and $\alpha \mathrm{\text{−}}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2{\mathrm{N}\mathrm{H}}_4\mathrm{H}\mathrm{g}(\mathrm{S}\mathrm{C}\mathrm{N}{)}_4$ (dashed lines) obtained at $T=4\mathrm{K}$ for the electric field polarized (a) parallel and (b) perpendicular to the $c$ axis. In both directions of $(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2\mathrm{K}\mathrm{H}\mathrm{g}(\mathrm{S}\mathrm{C}\mathrm{N}{)}_4$ a pseudogap feature is clearly seen at $200{\mathrm{c}\mathrm{m}}^{-1}$ which is not present in the superconductor $(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2{\mathrm{N}\mathrm{H}}_4\mathrm{H}\mathrm{g}(\mathrm{S}\mathrm{C}\mathrm{N}{)}_4$.

Figure 3

Evolution of optical conductivity as the intersite Coulomb repulsion $V/t$ increases. The results are obtained using exact diagonalization of an extended Hubbard model on a $4\times 4$ square lattice with fixed $U=20t$. A Lorentzian broadening of $0.4t$ is used for comparison with experimental data. A broad band at about $3V$ and a feature at its lower edge appear as a result of charge fluctuations associated with short range charge ordering. Note that for the plotted range of $V/t$, the system is on the metallic side of the transition: $V\ll V_c^{\mathrm{M}\mathrm{I}}\approx 2t$. The left axis is given in normalized units assuming $c=1$ and $\hslash =1$. For the right axis we used the numerical values ($c=10\AA$ and $4V_{\mathrm{m}\mathrm{o}\mathrm{l}}=2000{\AA }^3$) appropriate for $(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_{2}M\mathrm{H}\mathrm{g}(\mathrm{S}\mathrm{C}\mathrm{N}{)}_4$.