Electron doping and superconductivity in the two-dimensional Hubbard model

Abstract

An elaborate variational wave function is used for studying superconductivity in the repulsive twodimensional Hubbard model, including both nearest- and next-nearest-neighbor hoppings. A marked asymmetry is found between the “localized” hole-doped region and the more itinerant electron-doped region. Superconductivity with d-wave symmetry turns out to be restricted to densities where the Fermi surface crosses the magnetic zone boundary. A concomitant peak in the magnetic structure factor at , clearly points to a magnetic mechanism. One of the central issues in the field of high-temperature superconductors has been—and for some researchers still is—the question whether pairing in the cuprates arises from purely repulsive interactions, as proposed by Anderson two decades ago. 1 This question has been studied extensively in the framework of the two-dimensional 2Drepulsive Hubbard model and the related t-J model. Recent progress, both in dynamical mean-field theory 2,3 and in variational calculations, 4 has strengthened the case for the existence of a superconducting phase in the Hubbard model, with a d-wave gap parameter reasonably close to the experimental values for intermediate interaction strengths U of the order of the bandwidth. This conclusion has been challenged on the basis of Monte Carlo simulations, 5 which we believe to be not conclusive, as discussed below. Most previous studies of the Hubbard model have been restricted to nearest-neighbor hopping, where electron doping does not differ from hole doping. Here we show that the addition of second-neighbor hopping which breaks the electron-hole symmetry changes this behavior substantially. While the hole-doped side is “localized” and shows kineticenergy-driven superconductivity with a large condensation energy, the electron-doped side is itinerant with a potentialenergy-driven superconductivity and a small condensation energy.