Charge imbalance in $\lambda$-(BETS)$_2$GaCl$_4$ and their interplay with superconductivity

The two-dimensional organic superconductor $\lambda$-(BETS)$_2$GaCl$_4$ exhibits pronounced charge fluctuations below $T \approx 150$~K, in contrast to the sibling compound $\kappa$-(BETS)$_2$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 $\kappa$-salts. When the organic molecules are arranged in the $\lambda$-pattern, however, a strong vibrational $\nu_{27}(b_{1u})$ mode is present, that forms a narrow doublet. %indicating static charge imbalance of about 2\%. Most important, when cooling $\lambda$-(BETS)$_2$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 \l\ at $T_c=4.7$~K. We discuss the possibility of a charge-density-wave that coexists with the proposed spin-density-wave state.