Charge-ordering phenomena have been highly topical over the last few years. A phase transition towards a charge ordered state has been observed experimentally in several classes of materials. Among them, many studies have been devoted to the family o
f quasi-one dimensional organic charge-transfer salts (TMTTF)$_2$X, where (TMTTF) stands for tetramethyltetrathiafulvalene and X for a monovalent anion (X = PF$_6$, AsF$_6$ and SbF$_6$). However, the relationship between the electron localization phenomena and the role of the lattice distortion in stabilizing the charge-ordering pattern is poorly documented in the literature. Here we present a brief overview of selected literature results with emphasis placed on recent thermal expansion experiments probing the charge-ordering transition of these salts.
Several experimental studies have shown the presence of spatially inhomogeneous phase coexistence of superconducting and non superconducting domains in low dimensional organic superconductors. The superconducting properties of these systems are found
to be strongly dependent on the amount of disorder introduced in the sample regardless of its origin. The suppression of the superconducting transition temperature $T_c$ shows clear discrepancy with the result expected from the Abrikosov-Gorkov law giving the behavior of $T_c$ with impurities. Based on the time dependent Ginzburg-Landau theory, we derive a model to account for the striking feature of $T_c$ in organic superconductors for different types of disorder by considering the segregated texture of the system. We show that the calculated $T_c$ quantitatively agrees with experiments. We also focus on the role of superconducting fluctuations on the upper critical fields $H_{c2}$ of layered superconductors showing slab structure where superconducting domains are sandwiched by non-superconducting regions. We found that $H_{c2}$ may be strongly enhanced by such fluctuations.
Using a combination of Density Functional Theory, mean-field analysis and exact diagonalization calculations we reveal the emergence of a dimerized charge ordered state in TMTTF$_2$-PF$_6$ organic crystal. The interplay between charge and spin order
leads to a rich phase diagram. Coexistence of charge ordering with a structural dimerization results in a ferroelectric phase, which has been observed experimentally. The tendency to the dimerization is magnetically driven revealing TMTTF$_2$-PF$_6$ as a multiferroic material.
