1. LASSP, Department of Physics, Cornell University, Ithaca, New York 14853, USA
2. RIKEN, Wako, Saitama 351-0198, Japan
3. Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
4. Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
5. School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK
6. CMPMS Department, Brookhaven National Laboratory, Upton, New York 11973, USA
7. Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
8. Department of Physics, University of California, Berkeley, California 94720, USA

Correspondence to: J. C. Davis^1,6 Correspondence and requests for materials should be addressed to J.C.D. (Email: jcdavis@ccmr.cornell.edu).

Abstract

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₊ 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.

1. LASSP, Department of Physics, Cornell University, Ithaca, New York 14853, USA
2. RIKEN, Wako, Saitama 351-0198, Japan
3. Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
4. Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
5. School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK
6. CMPMS Department, Brookhaven National Laboratory, Upton, New York 11973, USA
7. Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
8. Department of Physics, University of California, Berkeley, California 94720, USA

Correspondence to: J. C. Davis^1,6 Correspondence and requests for materials should be addressed to J.C.D. (Email: jcdavis@ccmr.cornell.edu).

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