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Pseudogap and singlet formation in cuprate and organic superconductors

The pseudogap phase occurring in cuprate and organic superconductors is analyzed based on the dynamical cluster approximation (DCA) approach to the Hubbard model. A cluster embedded in a self-consistent bath is studied. With increasing Coulomb repulsion, U, the antinodal point [k=(pi,0)] displays a gradual suppression of spectral density of states around the Fermi energy which is not observed at the nodal point [k=(pi/2,pi/2)]. The opening of the antinodal pseudogap is related to the internal structure of the cluster and the much weaker bath-cluster couplings at the antinodal than nodal point. The role played by internal cluster correlations is elucidated from a simple four-level model. For small U, the cluster levels form Kondo singlets with their baths leading to a peak in the spectral density. As U is increased a localized state is formed localizing the electrons in the cluster. If this cluster localized state is non-degenerate, the Kondo effect is destroyed and a pseudogap opens up in the spectra at the anti-nodal point. The pseudogap can be understood in terms of destructive interference between different paths for electrons hopping between the cluster and the bath. However, electrons at the nodal points remain in Kondo states up to larger U since they are more strongly coupled to the bath. The strong correlation between the (pi,0) and (0,pi) cluster levels in the localized state leads to a large correlation energy gain which is important for localizing electrons and opening up a pseudogap. Such scenario is in contrast with two independent Mott transitions found in two-band systems with different bandwidths in which the localized cluster electron does not correlate strongly with any other cluster electron for intermediate U. The important intracluster sector correlations are associated with the resonating valence bond (RVB) character of the cluster.