Pressure-induced deconfinement of the charge transport in the quasi-one-dimensional Mott insulator ${\left(\mathrm{TMTTF}\right)}_2\mathrm{As}{\mathrm{F}}_6$

We studied the pressure dependence of the room-temperature infrared reflectivity of ${\left(\mathrm{TMTTF}\right)}_2\mathrm{As}{\mathrm{F}}_6$ along all three optical axes. This anisotropic organic compound consists of molecular stacks with orbital overlap along the $a$ direction; due to electronic correlations the system is a quasi-one-dimensional Mott insulator with a charge gap ${\Delta }_{\rho }\approx 70\mathrm{meV}$. The gap is gradually reduced with increasing external pressure, accompanied by the onset of a Drude contribution along the stacking direction. In the perpendicular $b^{\prime }$ direction a Drude-like optical response is observed for pressures above $2\mathrm{GPa}$. This behavior is interpreted in terms of a deconfinement of the electrons in a one-dimensional Mott insulator, i.e., an insulator-to-metal transition which occurs when the interchain transfer integral $t_b$ is approximately equal to half of the charge gap energy. We estimate the values of $t_b$ and the Luttinger liquid parameter $K_{\rho }$ as a function of pressure.

Figure 1

Schematic phase diagram of the deconfinement transition for a system of weakly coupled conducting chains according to Refs. 3, 9. Transition from a Mott insulator (MI) to a high-dimensional metallic (HDM) state occurs at $T=0$ when $t_{\perp }$ reaches a critical value $t_{\perp }^{*}$ (trajectory 1). At high enough temperature, the increase of $t_{\perp }$ leads to a transition from a Mott insulating to a 1D Luttinger liquid (LL) conducting state (trajectory 2) and finally to a dimensional crossover into an HDM state (trajectory 3). The temperature change at a fixed value $t_{\perp }$ may also lead to a transition from a Mott insulating to a LL state (trajectory 4), or to a dimensional crossover (trajectory 5). The horizontal dashed line indicates the path of our pressure study.

Figure 2

(Color online) Room temperature reflectivity spectra $R_{s\text{−}d}$ of ${\left(\mathrm{TMTTF}\right)}_2\mathrm{As}{\mathrm{F}}_6$ as a function of pressure for $\mathbf{E}\Vert a$, $\mathbf{E}\Vert b^{\prime }$, and $\mathbf{E}\Vert c^{*}$. Note the different pressure values for $\mathbf{E}\Vert a,b^{\prime }$, and $\mathbf{E}\Vert c^{*}$. The inset shows the normalized pressure-induced change of the reflectivity $\delta R_{s\text{−}d}\left(P\right)=R_{s\text{−}d}\left(P\right)∕R_{s\text{−}d}\left(P_{\min }\right)-1$ at $630{\mathrm{cm}}^{-1}$.

Figure 3

(a) Comparison of the measured reflectivity $R_{s\text{−}d}$ of ${\left(\mathrm{TMTTF}\right)}_2\mathrm{As}{\mathrm{F}}_6$ with the fits, according to Eqs. (2, 3), for $\mathbf{E}\Vert a$ for two pressures (0.5 and $3.0\mathrm{GPa}$). (b) Corresponding optical conductivity ${\sigma }_1\left(\omega \right)$ spectra from the fit compared with the optical conductivity obtained by the KK analysis.

Figure 4

(Color online) Room temperature optical conductivity ${\sigma }_1\left(\omega \right)$ spectra of ${\left(\mathrm{TMTTF}\right)}_2\mathrm{As}{\mathrm{F}}_6$ for $\mathbf{E}\Vert a$ as a function of pressure obtained by the KK analysis. Inset: Pressure dependence of the spectral weight $S$ according to Eq. (5).

Figure 5

(Color online) Room temperature optical conductivity ${\sigma }_1\left(\omega \right)$ spectra of various Bechgaard-Fabre salts for $\mathbf{E}\Vert a$: (a) ${\left(\mathrm{TMTTF}\right)}_2\mathrm{As}{\mathrm{F}}_6$ at $5.2\mathrm{GPa}$; (b) ${\left(\mathrm{TMTSF}\right)}_2\mathrm{Cl}{\mathrm{O}}_4$; (c) ${\left(\mathrm{TMTSF}\right)}_2\mathrm{P}{\mathrm{F}}_6$; (d) ${\left(\mathrm{TMTSF}\right)}_2\mathrm{As}{\mathrm{F}}_6$; (e) ${\left(\mathrm{TMTTF}\right)}_2\mathrm{Br}$; (f) ${\left(\mathrm{TMTTF}\right)}_2\mathrm{P}{\mathrm{F}}_6$; and (g) ${\left(\mathrm{TMTTF}\right)}_2\mathrm{As}{\mathrm{F}}_6$ at $0.5\mathrm{GPa}$. The spectra (b)–(f) are taken from Refs. 19, 38.

Figure 6

(Color online) The log-log scale plot of the optical conductivity spectra ${\sigma }_1\left(\omega \right)$ of ${\left(\mathrm{TMTTF}\right)}_2\mathrm{As}{\mathrm{F}}_6$ for $\mathbf{E}\Vert a$ at different pressures. The straight lines are fits according to Eq. (6). Inset: Power-law exponent $\gamma$ and corresponding LL exponent $K_{\rho }$ as a function of applied pressure.

Figure 7

(Color online) Room temperature reflectivity spectra $R_{s\text{−}d}$ of ${\left(\mathrm{TMTTF}\right)}_2\mathrm{As}{\mathrm{F}}_6$ for $\mathbf{E}\Vert b^{\prime }$ together with the Drude fit according to Eq. (7).

Figure 8

Calculated interchain transfer integral $t_b$ (open circles) and the charge gap ${\Delta }_{\rho }$ (closed circles) as a function of pressure for ${\left(\mathrm{TMTTF}\right)}_2\mathrm{As}{\mathrm{F}}_6$. The dashed lines are the linear fits of $t_b$ and $2t_b$. $P^{*}$ is the pressure at which the deconfinement transition takes place. The full line schematically shows the vanishing of $t_b$ at the transition pressure.