Competing Phases in High-Temperature Superconductors

High-Temperature superconducting materials (HTSC) are characterized by strong electronic correlations, which are responsible for a number of fascinating anomalous physical properties. Depending on temperature and doping, these materials show long-range ordered phases as well as regions of strong but short-range fluctuations. It is the central aim of the present theory project to achieve a significantly improved microscopic understanding of the HTSC and, in particular, of the doping dependence of their phase diagram, focusing on the question "what is of general relevance" and "what is more material-specific". In this project we plan to apply and to further develop two cluster methods in order to evaluate thermodynamic properties, phase boundaries, and excitation spectra of common model systems for the HTSC (one- and three-band Hubbard models).This project should be carried out in close contact with the newly established (DFG) Research Unit "Doping dependence of phase transitions and ordering phenomena in copper-oxide superconductors", and the results obtained within the present project should be compared with experimental results of the other groups (inelastic neutron scattering, angle-resolved photoemission-, tunneling-, and Raman-spectroscopy). Some of the many questions related to the physics of HTSC should be addressed in the present project: (i) the competition between long-range ordered phases as well as the effects of short-range fluctuations, (ii) the nature of the so-called pseudogap: is it different in electron-doped materials?, (iii) the phase diagram and the symmetry of the order parameter in electron-doped compounds, (iv) the role of phonons in HTSC, and (v) the anomalous behavior of the optical conductivity. With the help of the coordinated cooperation with the experimental groups of the Research Unit we expect to understand the global phase diagram of HTSC in the hole- and in the electron-doped compounds on the basis of a unifying picture of a doped Mott insulator.

Goal of the project was an improved understanding of microscopic properties of so-called High-Temperature superconductors (HTSC). Superconductors are materials which conduct current without energy dissipation when cooled below a certain temperature. The latter is relatively high for HTSC, namely about -150 Celsius in contrast to -250 Celsius for the more conventional "low" temperature superconductors. In particular, this project focuses on understanding the complex dynamics of charge carriers which is responsible for the phenomenon of superconductivity, but also for other unconventional properties (magnetic, optical, spectral, thermal, etc.). One of the most important aspects is to identify the mechanism, i. e. the "glue" which is responsible for the attraction between charge carries and for the formation of so called Cooper pairs, which are the building blocks of superconductivity. In this project, we obtained several results which support the hypothesis that magnetic fluctuations are the main responsible for this glue. These consist in interpretations of experimental data in terms of our numerical simulations. In an initial paper, we show that the occurrence of two gaps with different doping behavior, as observed experimentally in HTSC, can be explained in terms of a single phenomenon assuming a pairing interaction which is strongest for wave vectors corresponding to antiferromagnetic fluctuations. Also an analysis of polarized photon scattering data suggests the presence of strong scattering around the same wave vectors. Our numerical simulations provide a consistent picture of the phase diagram of HTSC, on the one hand, and of their magnetic spectrum, in particular the so- called "hourglass" dispersion, on the other. This dispersion can thus be considered as a fingerprint of magnetic fluctuations still present in the superconducting phase, and, thus, possibly contributing to the glue. While magnetic fluctuations are certainly important, several experimental results, stress the importance of the coupling of electron with lattice vibrations, i. e. phonons, which are the "glue" responsible for low temperature superconductivity. Results obtained within the present project support this idea by showing that vibrations of apical oxygens enhance the attraction between charge carrier, and therefore may partially contribute to the mechanism of superconductivity.