Depressed charge gap in the triangular-lattice Mott insulator $\kappa \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{C}\mathrm{N}\right)}_3$

We have investigated polarized optical conductivity for the triangular-lattice Mott insulator $\kappa \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{C}\mathrm{N}\right)}_3$ over the photon-energy range of $E=8\mathrm{meV}–5\mathrm{eV}$. This compound is located far from the metal-insulator phase boundary in the bandwidth-controlled phase diagram of $\kappa \text{−}{\left(\mathrm{ET}\right)}_{2}X$ salts and consequently strong charge correlations are expected. However, its ground-state optical conductivity spectrum for polarizations within the $bc$ plane shows no distinct charge gap in the energy range investigated, i.e., it is considerably smaller than $\Delta \approx 110\mathrm{meV}$, which was previously reported for the barely insulating $\kappa \text{−}{\left(\mathrm{ET}\right)}_2\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{C}\mathrm{N}\right)}_2\right]\mathrm{Cl}$ [Kornelsen et al., Solid State Commun. 81, 343 (1992)]. We attribute the pseudo-gap-like nature of the optical spectra to strong spin fluctuations emerging in an isotropic triangular lattice. The midinfrared peak is analyzed in terms of Coulomb interaction and $\kappa \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{C}\mathrm{N}\right)}_3$ is characterized by intermediate strength of electron correlation.

Figure 1

Arrhenius plot of the resistance of a $\kappa \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{C}\mathrm{N}\right)}_3$ single crystal. The gray dashed line at low temperature indicates the fitting of the gap value according to $R\left(T\right)=R_0\exp (\Delta ∕2k_{B}T)$. Inset: $\log \left(R\right)$ vs $\log \left(T\right)$ plot indicative of a power-law behavior of the resistance in the low-temperature region.

Figure 2

(Color online) Polarized reflectivity spectra of $\kappa \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{C}\mathrm{N}\right)}_3$ measured at various temperatures for $E\Vert c$ and $E\Vert b$ (upper and lower panel, respectively). The insets show the corresponding conductivity spectra at low temperature.

Figure 3

(Color online) Optical conductivity spectra of$\kappa \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{C}\mathrm{N}\right)}_3$ at the lowest and highest temperature of the measurement for $E\Vert c$ and $E\Vert b$ shown in the upper and lower panel, respectively. The temperature evolution of the dimer peak is enlarged in the insets.

Figure 4

(Color) Comparison of the low-temperature optical conductivity of $\kappa \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{C}\mathrm{N}\right)}_3$ and $\kappa \text{−}{\left(\mathrm{ET}\right)}_2\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{C}\mathrm{N}\right)}_2\right]\mathrm{Cl}$. For the former compound, the $T=10\mathrm{K}$ spectrum representative for the whole $T<100\mathrm{K}$ range is only displayed. The conductivity spectra for $\kappa \text{−}{\left(\mathrm{ET}\right)}_2\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{C}\mathrm{N}\right)}_2\right]\mathrm{Cl}$ are reproduced from Ref. 24. The left (right) scale corresponds to $\kappa \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{C}\mathrm{N}\right)}_3$ $\left(\kappa \text{−}{\left(\mathrm{ET}\right)}_2\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{C}\mathrm{N}\right)}_2\right]\mathrm{Cl}\right)$.