Quasiparticles at the Verge of Localization near the Mott Metal-Insulator Transition in a Two-Dimensional Material

The dynamics of charge carriers close to the Mott transition is explored theoretically and experimentally in the quasi-two-dimensional organic charge-transfer salt, $\kappa -(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2\mathrm{Cu}[\mathrm{N}(\mathrm{CN}{)}_2]{\mathrm{Br}}_x{\mathrm{Cl}}_{1-x}$, with varying Br content. The frequency dependence of the conductivity deviates significantly from simple Drude model behavior: there is a strong redistribution of spectral weight as the Mott transition is approached and with temperature. The effective mass of the quasiparticles increases considerably when coming close to the insulating phase. A dynamical mean-field-theory treatment of the relevant Hubbard model gives good quantitative description of experimental data.

Figure 1

Frequency dependence of the optical conductivity at several temperatures. Calculations are based on a DMFT treatment of the Hubbard model on the anisotropic triangular lattice. For $U=0.3\mathrm{eV}$, a gradual suppression of the Drude peak occurs with increasing temperature. The inset shows the effective number of charge carriers $N_{\mathrm{eff}}(\omega )$ per lattice site, calculated from the spectrum using Eqs. (4, 5).

Figure 2

Frequency dependence of the optical conductivity due to the correlated charge carriers of $\kappa -(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2\mathrm{Cu}[\mathrm{N}(\mathrm{CN}{)}_2]{\mathrm{Br}}_{0.73}{\mathrm{Cl}}_{0.27}$. Experimental data [15] are shown for conductivity in the layers ($E\parallel c$) at different temperatures. This data compares favorably with theoretical calculations presented in Fig. 1. The inset shows the effective number of charge carriers $N_{\mathrm{eff}}(\omega )$ per dimer.

Figure 3

Effective charge-carrier number per $(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2$ dimer approaching the Mott transition. In the left panel the results of a DMFT calculation of $N_{\mathrm{eff}}(\omega )$ (at a temperature of 50 K) show how the spectral weight is redistributed as one approaches the transition to the Mott insulating phase which occurs at $U=15|t_2|=0.45\mathrm{eV}$. The SW redistribution and saturation of $N_{\mathrm{eff}}(\omega )$ is in agreement with the experimental data for $\kappa -(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2\mathrm{Cu}[\mathrm{N}(\mathrm{CN}{)}_2]{\mathrm{Br}}_x{\mathrm{Cl}}_{1-x}$ for $x=0.73$, 0.85 (at low temperature) shown in the right panel. Typical error bars for the experimental data are shown.

Figure 4

Frequency dependence of the scattering rate and effective mass extracted from an extended Drude model analysis of the optical conductivity. (a) and (b) show the results of DMFT calculations for different $U/W$ and $T=50\mathrm{K}$. (c) and (d) show the experimental results for the same quantities at $T=5\mathrm{K}$. The inset of (a) shows how below a frequency ${\omega }^{*}\approx 400{\mathrm{cm}}^{-1}$ the scattering rate found for both experiment and theory has the quadratic frequency dependence expected for Fermi-liquid quasiparticles. Clearly as the Mott insulating phase is approached the effective mass and the scattering rate increase significantly.