Colloquia

It is already 21 years since high-temperature superconductivity (HTSC) in the cuprate was discovered by Müller and Bednorz. At the beginning many theoreticians, including several Nobel Laureates, claimed they knew the answer. Even today, they keep claiming so, while they acknowledge that they actually do not know how to solve the problem theoretically. In the mean time experimentalists succeeded in making impressive improvements of their capabilities, and we now know the remarkable details of the cuprates physics and the HTSC phenomena. What emerged from the vast amounts of experimental results is the realization that while the existing theories can describe parts of the observed phenomena, something fundamental appears to be lacking from the theory. The puzzle may be deeper than people prefer to admit. In my view one of the most fundamental problems is that the transition from the Mott-Hubbard insulator due to strong electron-electron interaction to the Fermi-liquid state is an abrupt one, while any mean-field approximation makes it falsely continuous. In this talk I discuss evidences from neutron scattering experiments that this transition involves nano-scale phase separation, reflecting the discontinuity in transition, and how this conflict could contribute to the HTSC phenomena.