Emanuel Gull, Olivier Parcollet, Andrew J. Millis
Lamellar perovskite-based copper oxide compounds display three remarkable properties: d-wave superconductivity, with unprecedentedly high transition temperatures, a nontrivial ('Mott') insulating state and a `pseudogap' regime of suppressed density of states. P. W. Anderson argued that these have a common origin as strong-correlation phenomena that could be understood in terms of the two-dimensional Hubbard model, but the interplay between the pseudogap and the superconductivity has remained controversial, with some authors suggesting the pseudogap is a signature of unusual superconducting fluctuations and others suggesting it is a competing phase or regime. Here we use new numerical techniques to solve the Hubbard model in the dynamical cluster approximation, which becomes exact as cluster size tends to infinity. Our methods enable the study of interactions strong enough and temperatures low enough to that the properties of the superconducting state and its relation to the Mott insulator and the pseudogap can be determined for clusters large enough to be representative of the thermodynamic limit and show that in the Hubbard model the two phenomena, while both linked to proximity to the Mott insulating state, are competing phenomena. Superconductivity is found to occur in a dome separated from the Mott insulating state by the pseudogap. The emergence of superconductivity from the pseudogap regime leads to a decrease in the gap (i.e. the creation of new states within the pseudogap), in agreement with recent angle-resolved photoemission data.
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http://arxiv.org/abs/1207.2490
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