Charge-order fluctuations and superconductivity in two-dimensional organic metals

We report comprehensive Raman and infrared investigations of charge-order (CO) fluctuations in the organic metal ${\beta }^{\prime \prime }$-(BEDT-TTF)${}_2$SF${}_5$CHFSO${}_3$ and superconductor ${\beta }^{\prime \prime }$-(BEDT-TTF)${}_2$SF${}_5$CH${}_2$CF${}_2$SO${}_3$. The charge-sensitive vibrational bands are analyzed through an extension of the well-known Kubo model for the spectral signatures of an equilibrium between two states. At room temperature, both salts exhibit charge fluctuations between two differently charged molecular states with an exchange frequency of about $6\times {10}^{11}{\mathrm{s}}^{-1}$. The exchange rate of the metallic salt remains roughly constant down to 10 K, while in the superconductor, the exchange velocity starts to decrease below 200 K, and a “frozen” charge-ordered state emerges and coexists with the charge-order fluctuation state down to the superconducting temperature. These findings are confronted with other spectroscopic experiments, and a tentative phase diagram is proposed for the ${\beta }^{\prime \prime }$ BEDT-TTF quarter-filled salts.

Figure 1

Layer of BEDT-TTF molecules in ${\beta }^{\prime \prime }$-SC viewed perpedicularly to the molecular long axis. The blue dots indicate the inversion centers, A and B label the two crystallographically independent molecular units. The organic anion layers are not shown. (Inset) Structure of BEDT-TTF molecule, with indication of the molecular axes.

Figure 2

Frequencies of the two charge-sensitive BEDT-TTF C=C stretching $a$ modes (${\nu }_3$ and ${\nu }_4$) as a function of the charge difference $\Delta \rho$ between the two inequivalent stacks. The red and blue curves correspond to the charge-poor ($\rho <0.5$) and charge-rich ($\rho >0.5$) molecules, respectively.

Figure 3

Raman spectra of ${\beta }^{\prime \prime }$-SC from 1200 to 1600 cm${}^{-1}$ at $T=300$ and 10 K. The spectra are offset for clarity.

Figure 4

Temperature dependence of infrared conductivity (left) and Raman spectra (right) of ${\beta }^{\prime \prime }$-SC. The spectra are offset for clarity. Note the different wave-number range in the IR and Raman spectra.

Figure 5

Temperature dependence of infrared conductivity (left) and Raman spectra (right) of ${\beta }^{\prime \prime }$-M. The spectra are offset for clarity. Note the different wave-number range in the IR and Raman spectra.

Figure 6

Fit of the IR conductivity (left) and of the Raman (right) spectra of ${\beta }^{\prime \prime }$-SC at $T=200$ K and at the lowest attained temperature. Blue crosses: experimental data; red line: overall spectral fit. The dashed orange lines correspond to Lorentzian fit of the bands not associated with the $b_1{\nu }_{22}$ (IR) and $a{\nu }_3$ (Raman). The green lines are fits of the $b_1{\nu }_{22}$ (IR) and $a{\nu }_3$ (Raman) with the band shape given by Eq. (2).

Figure 7

Fit of the IR conductivity (left) and of the Raman (right) spectra of ${\beta }^{\prime \prime }$-M at 200 K and at the lowest attained $T$. Blue crosses: experimental data; Red line: overall spectral fit. Dashed orange lines: Lorentzian fit of bands not associated with the $b_1{\nu }_{22}$ (IR) and $a{\nu }_3$ (Raman). Green lines: fit of the $b_1{\nu }_{22}$ (IR) and $a{\nu }_3$ (Raman) with the band shape given by Eq. (2).

Figure 8

(Top and middle) Charge difference $\Delta \rho$ and exchange velocity $v_{\mathrm{ex}}$ of ${\beta }^{\prime \prime }$-SC and ${\beta }^{\prime \prime }$-M as a function of temperature. The error bars in the middle panel are an estimate of the fitting uncertainty, based on the scattering of the various points. (Bottom) Normalized intensity of the $b_1{\nu }_{22}$ (fluctuating and frozen CO components) band and of the band associated with a lattice phonon around 40 cm${}^{-1}$.

Figure 9

Temperature dependence of the $b$-polarized in-plane conductivity spectra of ${\beta }^{\prime \prime }$-SC and ${\beta }^{\prime \prime }$-M measured in a wide frequency range. The inset visualizes the different contributions to the low-temperature conductivity (from Ref. [15]).

Figure 10

Tentative phase diagram for the members of the ${\beta }^{\prime \prime }$-(BEDT-TTF)${}_2$SF${}_{5}R$ SO${}_3$ family. ${\beta }^{\prime \prime }$-(BEDT-TTF)${}_2$SF${}_5$CH${}_2$SO${}_3$ (denoted ${\beta }^{\prime \prime }$-I) is a charge-ordered insulator, ${\beta }^{\prime \prime }$-(BEDT-TTF)${}_2$SF${}_5$CHFCF${}_2$SO${}_3$ (${\beta }^{\prime \prime }$-MI) undergoes a metal-insulator transition at 180 K, ${\beta }^{\prime \prime }$-(BEDT-TTF)${}_2$SF${}_5$CH${}_2$CF${}_2$SO${}_3$ (${\beta }^{\prime \prime }$-SC) is a superconductor at $T_c=5$ K, and ${\beta }^{\prime \prime }$-(BEDT-TTF)${}_2$SF${}_5$CHFSO${}_3$ (${\beta }^{\prime \prime }$-M) remains metallic down to low temperatures.