Electronic properties driven by strong correlation

4 Superconductivity and stripes in the t J model 73 4. D An important property of the projected BCS wavefunction 119 Bibliography 123 Introduction 1 Introduction The fascinating subject of superconductivity was opened over a century ago by Onnes [1], but until quite recently it was strictly a low-temperature phenomenon. The discovery of the cuprate superconductors [2] in a family of transition metal oxides, with transition temperatures up to T c 100K, has generated tremendous excitement for two main reasons. First, from a practical point of view, these compounds open a new temperature realm for superconducting devices which may have interesting commercial applications, and these potential benefits have attracted extraordinary attention from the whole scientific community. The second reason, relevant to those in a more abstract field, is the interest in the microscopic mechanism driving superconductivity. The first main distinction to be made is between theories which seek to describe these new materials within the framework of standard Eliashberg approach [3] or other weak coupling approaches arising from the exchange of other bosons, e.g. excitons or plasmons, and theories which make a radical break with the past and place these materials in the category of very strong coupling systems. It has become apparent from the early years of their discovery that many properties of these materials are unusual, and a proper understanding will require developing and extending concepts from many areas of condensed matter physics. The main characteristic of the superconducting state is the opening of a gap at the Fermi level in the electronic spectrum. The difference with the conventional supercon-ductors, where the gap opens isotropically along the Fermi surface, is that, for high-temperature superconductors, the gap has a strong dependence on the wavevector q, having a d x 2 y 2 symmetry. Nevertheless, the superconducting state appears to be associated with a pairing of electrons, and hence the overall superconducting behavior of these new systems is similar to the one of the conventional materials. In fact most of the familiar phenomena which are manifestations of the superconducting state (persistent current, Josephson tunneling, vortex lattice) have been established also in these materials , but, the microscopic mechanism underlying the high transition temperature is still mysterious. 2 Introduction There are theoretical problems connected not only with the high T c and with the microscopic mechanism of superconductivity, but also with the many unconventional electronic properties observed above T c , …