Non-Fermi Liquid Behavior in Nearly Charge Ordered Layered Metals

Non-Fermi liquid behavior is shown to occur in two-dimensional metals which are close to a charge ordering transition driven by the Coulomb repulsion. A linear temperature dependence of the scattering rate together with an increase of the electron effective mass occur above $T^{*}$, a temperature scale much smaller than the Fermi temperature. It is shown that the anomalous temperature dependence of the optical conductivity of the quasi-two-dimensional organic metal $\alpha \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_{2}M\mathrm{Hg}(\mathrm{SCN}{)}_4$, with $M={\mathrm{NH}}_4$ and Rb, above $T^{*}=50–100\mathrm{K}$, agrees qualitatively with predictions for the electronic properties of nearly charge ordered two-dimensional metals.

Figure 1

Non-Fermi liquid behavior in a metal close to charge ordering. The $T\mathrm{\text{−}}V$ phase diagram of the $3/4$-filled extended Hubbard model for $U=2|t|$ is shown. At $T=T_{\mathrm{CO}}$ a transition to the checkerboard CO phase occurs [large shaded region on the right side (blue online)]. The low temperature scale, $T^{*}$, separates Fermi liquid (FL) behavior at low temperatures from non-Fermi liquid (NFL) above $T^{*}$. A transition to a $2{\mathbf{k}}_F$ CDW occurs close to CO [small light shaded wedge starting at 1.4 (yellow online)].

Figure 2

Softening of the ${\mathbf{q}}_c=(\pi ,\pi )$ mode induced by temperature close to the charge ordering transition for $U=2|t|$ and $V=1.25|t|$. It is this $T$ dependence of the charge susceptibility which amplifies the self-energy corrections with increasing temperature leading to anomalous thermal increase of effective masses.

Figure 3

Temperature dependence of self-energy for $U=2|t|$ and $V=1.25|t|$. In (a) the imaginary part of the self-energy is plotted displaying the enhancement for $\omega <0$ with temperature, while in (b) the real part shows the gradual increase of the slope at the Fermi energy above $T^{*}$.

Figure 4

Anomalous electron effective mass enhancement induced by temperature and non-Fermi liquid behavior in a nearly charge ordered metal above $T^{*}$. In (a) the temperature dependence of the effective mass enhancement is shown for $U=2|t|$ and different $V$’s close to CO while in (b) the $T$ dependence of the scattering rate shows a linear $T$ dependence above $T^{*}$.

Figure 5

Temperature dependence of one-electron properties obtained from optical measurements on $\alpha \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_{2}M\mathrm{Hg}(\mathrm{SCN}{)}_4$ for the polarization parallel to the BEDT-TTF stacks. The thermal increase of effective mass enhancement (a) and the linear $T$-dependence of the scattering rate (b) observed above $T>T^{*}\approx 50–100\mathrm{K}$ agrees qualitatively with RPA predictions of nearly two-dimensional charge ordered metals.