How cooper pairs vanish approaching the Mott insulator in Bi₂Sr₂CaCu₂O₈+δ

The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons ( hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space ( k- space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the mysterious 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi- particles - the excitations resulting from the breaking of Cooper pairs should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi2Sr2CaCu2O8+delta in r- space and k- space simultaneously. We find that although the low- energy excitations are indeed Bogoliubov quasi- particles, they occupy only a restricted region of k- space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r- space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy- independent way. We demonstrate that these unusual r- space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k- space, to be replaced by locally translational- and rotational- symmetry- breaking pseudogap states in r- space.