superconductivity ∗

We present a 2+1-dimensional lattice model for the copper oxide superconductors and their parent compounds, in which both the charge and spin degrees of freedom are treated dynamically. The spin-charge coupling parameter is associated to the doping fraction in the cuprates. The model is able to account for the various phases of the cuprates and their properties, not only at low and intermediate doping but also for (highly) over-doped compounds. We acquire a qualitative understanding of high-Tc superconductivity as a Bose-Einstein condensation of bound charge pairs. The discovery of the new perovskite supercon-ductors [1] opened the path to critical temperatures (T c) for superconductivity as high as 140 K, surpassing by a factor of seven the highest known T c for metals or alloys. In fact the physical mechanism for superconductivity seems to be rather different. Traditional superconductors present an isotope effect, which calls for a phonon mediated mechanism. They also have a gap (of order of meV) in the excitation spectrum, as shown by the exponential decrease of the specific heat at low temperature. All this can be accounted for by the BCS theory, where electrons of opposite spin and momenta are attractively coupled through a phonon exchange. The basic BCS statement is the existence of a critical temperature at which this attraction simultaneously produces the formation of bound states of pairs of electrons (with binding energy of the order of the gap) and the condensation of those pairs into a quantum liquid. The new superconductors show an intriguing phenomenology: • Superconductivity appears in doped, ce