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

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+δ 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.

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Figure 1: Two classes of electronic excitations in copper oxides as p  → 0.
Figure 2: BQP interference.
Figure 3: Extinction of BQP interference.
Figure 4: Imaging copper oxide pseudogap excitations as p  → 0.
Figure 5: Bipartite electronic structure of copper oxides as p  → 0.

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Acknowledgements

We acknowledge and thank A. V. Balatsky, J. C. Campuzano, E. Fradkin, A. Georges, T. Hanaguri, P. J. Hirschfeld, S. Kivelson, E.-A. Kim, G. Kotliar, P. A. Lee, M. Norman, P. Phillips, M. Randeria, T. M. Rice, S. Sachdev, K. Shen, Z. X. Shen, A. Tsvelik, M. Vojta and F. C. Zhang for discussions. This work was supported by the US National Science Foundation through the Cornell Center for Material Research, by Brookhaven National Laboratory, by the US Department of Energy, by the US Office of Naval Research, by a Grant-in-Aid for Scientific Research from the Ministry of Science and Education (Japan), and by the 21st Century COE Program of the Japan Society for the Promotion of Science. P.W. acknowledges support from the Humboldt Foundation and A.S. acknowledges support from the US Army Research Office.

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Correspondence to J. C. Davis.

Supplementary information

Supplementary Information

This file contains Supplementary Methods; Supplementary Tables S1-S4; Supplementary Discussion; additional references and Supplementary Figures S1-S7 with Legends. This file includes the detailed methods used to extract quasiparticle momentum space properties from the Fourier transform of real space data. It includes tables of the doping dependence of various extracted parameters as well as a discussion of the impact of the doping dependence of the Bogoliubov arc end points on non-dispersive wavevectors. This Supplementary Figures illustrate the doping dependence of the properties depicted in the main text figures. (PDF 1057 kb)

Supplementary Video 1

This movie shows the Fourier transform of the real space conductance ratio maps for the TC = 88K sample of Bi2Sr2CaCu2O8+δ. It demonstrates strongly dispersing wave vectors at low bias voltages and non-dispersive wave vectors at high bias voltages. (MPG 1561 kb)

Supplementary Video 2

This movie shows the Fourier transform of the real space conductance ratio maps for the TC = 74K sample of Bi2Sr2CaCu2O8+δ. It demonstrates strongly dispersing wave vectors at low bias voltages and non-dispersive wave vectors at high bias voltages. (MPG 1561 kb)

Supplementary Video 3

This movie shows the Fourier transform of the real space conductance ratio maps for the TC = 45K sample of Bi2Sr2Ca0.8Dy0.2Cu2O8+δ. It demonstrates strongly dispersing wave vectors at low bias voltages and non-dispersive wave vectors at high bias voltages (MPG 1175 kb)

Supplementary Video 4

This movie shows shoes the Fourier transform of the real space conductance ratio maps for the TC = 20K sample of Bi2Sr2Ca0.8Dy0.2Cu2O8+δ. It demonstrates strongly dispersing wave vectors at low bias voltages and non-dispersive wave vectors at high bias voltages. (MPG 684 kb)

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Kohsaka, Y., Taylor, C., Wahl, P. et al. How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+δ. Nature 454, 1072–1078 (2008). https://doi.org/10.1038/nature07243

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