At the frontiers of phonons and correlated electrons

The interplay between strong electron-electron and electron-phonon interaction is extremely important in many materials. There are several studies on this subject but the most challenging issues, particularly those related to non-local spatial correlations, are hitherto poorly understood. Strong electronic correlations dramatically alter even the most popular effects of phonons in solids, such as superconductivity: The non-standard and puzzling phenomena occurring in high-temperature superconducting cuprates are mainly due to strong electronic correlations. Furthermore, the concomitant presence of electron-phonon and electron-electron interaction, if better rationalized, could be exploited to improve the efficiency in the heat conversion of novel thermoelectric materials based on strongly correlated electron systems. The first focus of the ``PHOCO`` proposal is hence the role of the electron-phonon interaction in high-temperature superconducting copper oxides, a long-standing and unresolved issue, which is currently again in the spotlight because of new exciting experimental evidences. The second focus, strongly correlated thermoelectrics based on transition metal compounds, oxides and heavy Fermion systems, is a new and hardly explored field with a high potential for applications. A major role in all these materials is played by short-range spatial correlations. Quantum cluster methods have been tailored for this type of correlations and have therefore recently superseded many of the previous approaches to strongly correlated systems. The two main flavors, namely the Dynamical Cluster Approximation (DCA) and Cellular Dynamical Mean Field Theory (CDMFT) are also very powerful as they can deal with realistic types of lattice vibrations. Hence it is possible to address the issue of the anomalously strong coupling to oxygen breathing phonons observed in the cuprates. Density Functional Theory, state-of-the-art method if correlations are not too strong, yields a very weak electron-phonon coupling. However, correlation effects seem to be extremely important for these phonon modes. Therefore DCA and CDMFT are expected to be in much better agreement with experiments. For a realistic description, many-body calculations and ab-initio methods can also be combined. In particular in the case of strongly-correlated thermoelectrics this will pave the way for a better understanding of their key characteristics.