Charge imbalance in $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ and their interplay with superconductivity

The two-dimensional organic superconductor $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ exhibits pronounced charge fluctuations below $T\approx 150$ K, in contrast to the sibling compound $\kappa -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ that remains metallic down to milli-Kelvin. Infrared spectroscopy reveals only minor splitting in the vibrational features of the latter compound, common to other strongly dimerized $\kappa$-type salts. When the organic molecules are arranged in the $\lambda$-type pattern, however, a strong vibrational ${\nu }_{27}\left(b_{1u}\right)$ mode is present that forms a narrow doublet. Most important, when cooling $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ below 150 K, two weak side modes appear due to charge disproportionation that amounts to $2\delta =0.14e$. In analogy to the ${\beta }^{\prime \prime }$-type organic conductors, we propose that charge fluctuations play an important role in emerging of unconventional superconductivity in $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ at $T_c=4.7$ K. We discuss the possibility of a charge-density wave that coexists with the proposed spin-density-wave state.

Figure 1

(a) Looking along $ac$ planes, the two-dimensional charge-transfer salts form different dimer patterns. In the $\kappa$ phase the dimers are rotated with respect to each other, while the $\lambda$-type pattern is organized in stacks with two dimers, i.e., four molecules per unit cell. (b) The BETS donor layers are separated by layers of ${\mathrm{GaCl}}_4^{-}$ anions. The organic molecules are slightly tilted in alternating directions in case of $\kappa$-BETS, while uniform in case of $\lambda$-BETS. (c) Most common are the donor molecules ET = BEDT-TTF, i.e., bis(ethylenedithio)tetrathiafulvalene), but sulfur can be substituted by selenium, leading to STF = BEDT-STF, and BETS = BEDT-TSF, i.e., bis(ethylenedithio)tetraselenafulvalene). The more extended selenium orbitals cause a larger bandwidth favoring metallic conductivity.

Figure 2

(a) Double logarithmic plot of the relative resistivity $\rho \left(T\right)/\rho \left(295K\right)$ of $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ (blue dots) and $\kappa -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ (red circles) measured as a function of temperature along the most conducting axes. The maximum in $\rho \left(T\right)$ for $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ can be best determined from the zero crossing of the derivative $\mathrm{d}\rho /\mathrm{d}T$ at $T_{\max }$ plotted in panel (b) using arbitrary units. The superconducting transition occurs at $T_c=4.7$ K as illustrated in panel (c).

Figure 3

Out-of-plane optical conductivity of (a) $\kappa -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ and (b) $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ in the spectral range of the ${\nu }_{27}\left(b_{1u}\right)$ mode measured in the temperature range from 295 to 9 K. For clarity reasons, the curves are shifted with respect to each other. While for $\kappa -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ two ${\nu }_{27}$-related peaks are observed at low temperatures, which are gradually smeared out upon warming up; there are two additional satellite features ($★$) identified in the $\lambda$-type salts, which appear only below approximately 150 K.

Figure 4

Analysis of the vibrational feature ${\nu }_{27}\left(b_{1u}\right)$. (a) Comparison of the low-temperature ($T=9$ K) optical conductivity of $\kappa -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ and $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ in the range of the charge-sensitive ${\nu }_{27}\left(b_{1u}\right)$ modes. For $\kappa -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ (red) a splitting of approximately 9 ${\mathrm{cm}}^{-1}$ occurs due to the double-layer structure. In the case of $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$ (blue), the pronounced doublet at 1459.1 and 1462.7 ${\mathrm{cm}}^{-1}$ results from crystallographically distinct molecules; the static separation is temperature independent. In addition two broad modes appear at 1453.5 and 1473 ${\mathrm{cm}}^{-1}$ due to fluctuating charge. (b) Temperature evolution of peak positions. The red crosses correspond to the modes of $\kappa -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$. The blue solid dots represent the fluctuating modes of $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$, while the open blue circles are related to the static modes of this compound. (c) Temperature dependent charge imbalance $2\delta$ for $\lambda -{\left(\mathrm{BETS}\right)}_2{\mathrm{GaCl}}_4$, calculated from the resonance frequencies of panel (b). (d) Linewidth of all modes plotted as a function of temperature on a logarithmic scale.