Electronic properties of correlated metals in the vicinity of a charge-order transition: Optical spectroscopy of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}M\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ ($M=\mathrm{N}{\mathrm{H}}_4$, Rb, Tl)

The infrared spectra of the quasi-two-dimensional organic conductors $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}M\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ ($M=\mathrm{N}{\mathrm{H}}_4$, Rb, Tl) were measured in the range from $50\text{to}7000{\mathrm{cm}}^{-1}$ down to low temperatures in order to explore the influence of electronic correlations in quarter-filled metals. The interpretation of electronic spectra was confirmed by measurements of pressure dependent reflectance of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{K}\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ at $T=300\mathrm{K}$. The signatures of charge order fluctuations become more pronounced when going from the $\mathrm{N}{\mathrm{H}}_4$ salt to Rb and further to Tl compounds. On reducing the temperature, the metallic character of the optical response in the $\mathrm{N}{\mathrm{H}}_4$ and Rb salts increases, and the effective mass diminishes. For the Tl compound, clear signatures of charge order are found albeit the metallic properties still dominate. From the temperature dependence of the electronic scattering rate the crossover temperature is estimated below which the coherent charge carriers response sets in. The observations are in excellent agreement with recent theoretical predictions for a quarter-filled metallic system close to charge order.

Figure 1

(Color online) Reflectivity and conductivity spectra of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{N}{\mathrm{H}}_4\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ at $T=300$, 200, 100, and $6\mathrm{K}$; left panels (a) and (b): $E\Vert$ stacks, right panels (c) and (d): $E\perp$ stacks. The insets show optical conductivity in the range of ${\nu }_{12}\left(A_g\right)$ and ${\nu }_{13}\left(A_g\right)$ modes. The inset in (d) shows the contributions of one Drude and two Lorentz components for $E\Vert$ stacks 300 and $6\mathrm{K}$.

Figure 2

(Color online) Reflectivity and conductivity spectra of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{Rb}\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ at $T=300$, 200, 100, and $6\mathrm{K}$; left frames (a) and (b): $E\perp$ stacks, right frames (c) and (d): $E\Vert$ stacks. The inset on (b) show optical conductivity in the range of ${\nu }_{12}\left(A_g\right)$ and ${\nu }_{13}\left(A_g\right)$ modes. The inset in (d) present the optical conductivity of the three salts in $E\Vert$ stacks at $6\mathrm{K}$ in log scale. The low-frequency part presented in dashed lines was received after smoothing the reflectivity data, a respective error bar at $60{\mathrm{cm}}^{-1}$ is shown.

Figure 3

(Color online) Reflectivity and conductivity spectra of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{Tl}\mathrm{Hg}{\left(\mathrm{S}\mathrm{C}\mathrm{N}\right)}_4$ at $T=300$, 200, 100, and $6\mathrm{K}$; panels (a) and (b): $E\perp$ stacks, panels (c) and (d): $E\Vert$ stacks. The inset show optical conductivity in the range of ${\nu }_{12}\left(A_g\right)$ and ${\nu }_{13}\left(A_g\right)$ modes.

Figure 4

(Color online) Reflectivity and conductivity spectra of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{K}\mathrm{Hg}{\left(\mathrm{S}\mathrm{C}\mathrm{N}\right)}_4$ at 0, 3, 5, 7, and $10\mathrm{kbar}$. Left panels, (a) and (b): $E\Vert$ stacks, right panels, (c) and (d): $E\perp$ stacks. The spectral region between 1700 and $2500{\mathrm{cm}}^{-1}$ is cut out from the spectra since it is affected by the strong absorbance of the diamond cell window. Arrows indicate the changes with increasing pressure. The inserts show the pressure dependence of the spectral weight of the Drude contribution (solid squares), the $1000\text{−}{\mathrm{cm}}^{-1}$ maximum (open squares), and the midinfrared band (open circles).

Figure 5

Upper panel: temperature dependence of the total spectral weight for $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}M\mathrm{Hg}{\left(\mathrm{S}\mathrm{C}\mathrm{N}\right)}_4$ ($M=\mathrm{N}{\mathrm{H}}_4$, Rb, Tl) parallel to the stacks (diagonal crosses) and perpendicular to the stacks (straight crosses). Lower panel: Temperature dependence of the spectral weight for the three main features in the optical spectra of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}M\mathrm{Hg}{\left(\mathrm{S}\mathrm{C}\mathrm{N}\right)}_4$ ($M=\mathrm{N}{\mathrm{H}}_4$, Rb, Tl) compounds. Filled squares: Drude peak, empty squares: $1000{\mathrm{cm}}^{-1}$ maximum, empty circles: $2500{\mathrm{cm}}^{-1}$ maximum. (a) Polarization parallel to the stacks direction and (b) perpendicular to the stacks. Note different scales for the different contributions and polarizations.

Figure 6

Temperature dependence of the $m^{*}∕m_b$ (upper panel) and Drude-scattering rate $\gamma$ (lower panel) for $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}M\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ ($M=\mathrm{N}{\mathrm{H}}_4$, Rb, Tl) compounds. Filled squares: $E\perp$ stacks, empty squares $E\Vert$ stacks. For the Tl salt a $\gamma \sim T^2$ fit of the scattering rate is shown with a dashed line.

Figure 7

The $T=6\mathrm{K}$ spectra of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{Tl}\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ (thick line) and $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{N}{\mathrm{H}}_4\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ (thin line) in $E\Vert$ stacks polarization. The inset shows the spectral range with ${\nu }_{12}\left(A_g\right)$ and ${\nu }_{13}\left(A_g\right)$ EMV-coupled features for these two spectra. For $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{Tl}\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ to electronic band at $1000{\mathrm{cm}}^{-1}$ has higher intensity, and the vibrational features ar split, pointing on an ordered state.

Figure 8

(Color online) Phase diagram for the quarter-filled two-dimensional organic conductors $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}M\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ ($M=\mathrm{N}{\mathrm{H}}_4$, K, Rb, Tl). With increasing pressure the effective intersite Coulomb repulsion $V∕t$ is reduced. At intermediate temperatures the system is tuned from a charge-order (CO) state to a metal with charge fluctuations in between. We propose that the compounds with $M=\mathrm{K}$, Tl are to be found in this part of the phase diagram. We propose that the Rb salt has lower influence of correlations, and the $\mathrm{N}{\mathrm{H}}_4$ salt is even less correlated, distinctly showing the increase of metallic properties on cooling, and becoming superconducting (SC) below $1\mathrm{K}$.