Low-dimensional organic and inorganic superconductors

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There is a consensus generalis about the impact of reducing the spatial dimension in systems of interacting electrons: quantum mechanical nature of matter is magnified and range of collective states expanded. This is a consequence of interactions between electrons, these elementary constituents of matter, which in reduced dimensions can behave in a highly organized and collective way. This is best exemplified in several classes of materials, in particular the so-called unconventional superconductors like the organic conductors, high-temperature cuprates, pnictides, . They are thus called, because besides carrying electricity without resistance like in simple metals such as mercury, aluminium, at sufficiently low temperature, superconductivity is found to emerge in the close proximity of other states of matter where electrons order collectively from their magnetic moments or their electric charges, leading for instance to magnetism or charge modulated structures.******The present five-year project is devoted to the theoretical description of the broad class of low dimensional organic and inorganic superconductors. In these weakly coupled chains systems, by tuning parameters such as external pressure or chemical constituents, correlated superconductivity can emerge from the competition with other states of matter like anti ferromagnetism, charge-density-wave or even a purely one-dimensional - Luttinger - quantum liquid. Such a pattern of phases, which in many aspects is a common feature of broader classes of unconventional superconductors, is essentially governed by law of quantum mechanics; its understanding represents a major challenge in condensed matter physics. *** One broad class of objectives of the project falls within the level of methodology, by further expanding renormalization group tools for which we have developed extensive experience in the last few years. This method is particularly suited for these low-dimensional correlated superconductors that are characterized by not too strong interactions. We think that in pursuing this program, we can firmly establish that the method can give us the main ingredients for a theory of correlated low dimensional superconductors that has predictive power. All the methodological developments serve to focus on the explanation of experimental results. *** **