Transformation of the superconducting gap to an insulating pseudogap at a critical hole density in the cuprates

We apply the recent wave-packet formalism developed by Ossadnik to describe the origin of the short-range ordered pseudogap state as the hole doping is lowered through a critical density in cuprates. We argue that the energy gain that drives this precursor state to Mott localization, follows from maximizing umklapp scattering near the Fermi energy. To this end, we show how energy gaps driven by umklapp scattering can open on an appropriately chosen surface, as proposed earlier by Yang, Rice, and Zhang. The key feature is that the pairing instability includes umklapp scattering, leading to an energy gap not only in the single-particle spectrum but also in the pair spectrum. As a result the superconducting gap at overdoping is turned into an insulating pseudogap in the antinodal parts of the Fermi surface.