On-chain electrodynamics of metallic $(\mathrm{TMTSF}{)}_{2}X$ salts: Observation of Tomonaga-Luttinger liquid response

We have measured the electrodynamic response in the metallic state of three highly anisotropic conductors, $(\mathrm{TMTSF}{)}_{2}X,$ where $X={\mathrm{PF}}_6$, ${\mathrm{AsF}}_6,$ or ${\mathrm{ClO}}_4,$ and TMTSF is the organic molecule tetramethyltetraselenofulvalene. In all three cases we find dramatic deviations from a simple Drude response. The optical conductivity has two features: a narrow mode at zero frequency, with a small spectral weight, and a mode centered around 200 ${\mathrm{}\mathrm{cm}}^{-1},$ with nearly all of the spectral weight expected for the relevant number of carriers and single particle bandmass. We argue that these features are characteristic of a nearly one-dimensional half- or quarter-filled band with Coulomb correlations, and evaluate the finite-energy mode in terms of a one-dimensional Mott insulator. At high frequencies $(ħ\omega >t_{\perp },$ the transfer integral perpendicular to the chains), the frequency dependence of the optical conductivity ${\sigma }_1\left(\omega \right)$ is in agreement with calculations based on an interacting Tomonaga-Luttinger liquid, and is different from what is expected for an uncorrelated one-dimensional semiconductor. The zero-frequency mode shows deviations from a simple Drude response, and can be adequately described with a frequency-dependent mass and relaxation rate.