Deconfinement transition and dimensional crossover in the Bechgaard-Fabre salts: Pressure- and temperature-dependent optical investigations

The infrared response of the organic conductor ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ and the Mott insulator ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ are investigated as a function of temperature and pressure and for the electric field polarized parallel and perpendicular to the molecular stacks. By applying external pressure on ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$, the Mott gap rapidly diminishes until the deconfinement transition occurs when the gap energy is approximately twice the interchain transfer integral. In its deconfined state ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ exhibits a crossover from a quasi-one-dimensional to a higher-dimensional metal upon reducing the temperature. For ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ this dimensional crossover is observed either with increase in external pressure or with decrease in temperature. We quantitatively determine the dimensional crossover line in the pressure-temperature diagram based on the degree of coherence in the optical response perpendicular to the molecular stacks.

Figure 1

(Color online) Schematic phase diagram of the deconfinement transition for a system of weakly coupled chains according to Refs. 3, 7. The transition from a Mott insulator (MI) to a high-dimensional metallic (HDM) state occurs at $T=0$ when the transverse hopping integral $t_{\perp }$ reaches a critical value $t_{\perp }^{\ast }$. At high-enough temperature, the increase in $t_{\perp }$ leads to a transition from a Mott insulator to a 1D Luttinger-liquid (LL) state and, with further increase in $t_{\perp }$ to a dimensional crossover to a HDM.

Figure 2

Pressure-dependent unit-cell volume of ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ (open circles) and ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ (full rectangles) at room temperature. The lines represent the fits according to the Birch equation of state, Eq. (1).

Figure 3

(Color online) Pressure-dependent reflectivity spectra $R_{s\text{−}d}$ of ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ and ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ measured at room temperature for the polarization $\mathbf{E}\parallel a$.

Figure 4

(Color online) Real part of the optical conductivity ${\sigma }_1$ of ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ and ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ obtained from the room-temperature reflectivity for the polarization $\mathbf{E}\parallel a$. For clarity reason the phonon contributions are subtracted; examples of the complete conductivity spectra of ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ and ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ at low pressure are plotted in the insets. The dashed lines illustrate the method used to determine the Mott gap.

Figure 5

(Color online) Pressure-dependent reflectivity spectra $R_{s\text{−}d}$ of ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ and ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ measured at room temperature for the polarization $\mathbf{E}\parallel b^{\prime }$.

Figure 6

(Color online) Pressure-dependent reflectivity spectra $R_{s\text{−}d}$ of ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ for the electric field polarized normal to the stacks, $\mathbf{E}\parallel b^{\prime }$, (a) at room temperature, (b) at 200 K, and (c) at 20 K. The vertical dotted line marks the frequency of $610{\text{cm}}^{-1}$ at which the reflectivity change $\delta R_{s\text{−}d}$ is estimated (see Fig. 7). The solid lines are fits with a Drude term combined with Fano oscillators.

Figure 7

(Color online) Normalized pressure-induced change in the reflectivity level of ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ for $\mathbf{E}\parallel b^{\prime }$ at $610{\text{cm}}^{-1}$ at different temperatures as indicated. The dashed line is a guide to the eye.

Figure 8

(Color online) Pressure-dependent reflectivity spectra $R_{s\text{−}d}$ of ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ for $\mathbf{E}\parallel b^{\prime }$ (a) at room temperature, (b) at 100 K, and (c) at 25 K. The solid lines are fits with a Drude term combined with Fano oscillators.

Figure 9

(Color online) Real part of the optical conductivity ${\sigma }_1$ of (a) ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ and (b) ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ obtained from the fits of room-temperature reflectivity for the polarization $\mathbf{E}\parallel b^{\prime }$. Insets show the respective spectral weight as a function of pressure obtained according to Eq. (3) when integrating up to $8000{\text{cm}}^{-1}$.

Figure 10

(Color online) Pressure dependence of the Mott gap energy ${\Delta }_{\rho }$ and the transverse hopping integral $2t_b$ for ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ and ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ salts as obtained from the room-temperature data. The upper pressure scale corresponds to ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ and is shifted by 3 GPa with respect to the lower pressure scale for the ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ salt.

Figure 11

(Color online) Comparison of the room-temperature reflectivity spectra $R_{s\text{−}d}$ of ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ along and perpendicular to the stacks as pressure increases. The arrows indicate the major changes in the spectra with increasing pressure.

Figure 12

(Color online) Loss function of the Drude response perpendicular to the conducting stacks $\left(\mathbf{E}\parallel b^{\prime }\right)$ in ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$: (a) at 0.1 GPa and three selected temperatures; (b) at 200 K and three selected pressures.

Figure 13

(Color online) The coherence parameter of the interstack charge transport ${\kappa }_b$ as a function of temperature and pressure for ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$. The solid line corresponds to ${\kappa }_b=0.85$. The circles illustrate the line of the dimensional crossover determined from transport measurements by Moser et al. (Ref. 20). The dotted line is a guide to the eye. The asterisks mark the measurement points.

Figure 14

(Color online) The coherence parameter of the interstack charge transport ${\kappa }_b$ as a function of temperature and pressure for ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$. The solid line corresponds to ${\kappa }_b=0.85$. The asterisks mark the measurement points.

Figure 15

(Color online) Temperature-pressure phase diagram of the Bechgaard-Fabre salts under investigation. The symbols represent the phase boundaries determined in this work: the deconfinement transition (solid circles) from the MI into the 1D LL, and the dimensional crossover (open squares) from the LL to the HDM state. For ${\left(\text{TMTTF}\right)}_2{\text{PF}}_6$ and ${\left(\text{TMTSF}\right)}_2{\text{PF}}_6$ the ambient-pressure positions are indicated.