The influence of Mott physics on the doping–temperature phase diagram of copper oxides represents a major issue that is the subject of intense theoretical and experimental efforts. Here, we investigate the ultrafast electron dynamics in prototypical single-layer Bi-based cuprates at the energy scale of the O-2p → Cu-3d charge-transfer (CT) process. We demonstrate a clear evolution of the CT excitations from incoherent and localized, as in a Mott insulator, to coherent and delocalized, as in a conventional metal. This reorganization of the high-energy degrees of freedom occurs at the critical doping pcr ≈ 0.16 irrespective of the temperature, and it can be well described by dynamical mean-field theory calculations. We argue that the onset of low-temperature charge instabilities is the low-energy manifestation of the underlying Mottness that characterizes the p < pcr region of the phase diagram. This discovery sets a new framework for theories of charge order and low-temperature phases in underdoped copper oxides.
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Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane
Nature Communications Open Access 26 January 2021
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Lee, P. A. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).
Phillips, P. Mottness. Ann. Phys. 321, 1634–1650 (2006); July 2006 Special Issue.
Abbamonte, P. et al. Spatially modulated “Mottness” in La2−xBaxCuO4 . Nat. Phys. 1, 155–158 (2005).
Fradkin, E. & Kivelson, S. High-temperature superconductivity: ineluctable complexity. Nat. Phys. 8, 864–866 (2012).
Alloul, H. What is the simplest model that captures the basic experimental facts of the physics of underdoped cuprates? C. R. Phys. 15, 519–524 (2014).
Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).
Emery, V. & Kivelson, S. Frustrated electronic phase separation and high-temperature superconductors. Physica C 209, 597–621 (1993).
Castellani, C., Di Castro, C. & Grilli, M. Singular quasiparticle scattering in the proximity of charge instabilities. Phys. Rev. Lett. 75, 4650–4653 (1995).
Kivelson, S. A., Fradkin, E. & Emery, V. J. Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998).
Ghiringhelli, G. et al. Long-range incommensurate charge fluctuations in (Y, Nd)Ba2Cu3O6+x . Science 337, 821–825 (2012).
Achkar, A. J. et al. Distinct charge orders in the planes and chains of ortho-iii-ordered YBa2Cu3O6+δ superconductors identified by resonant elastic X-ray scattering. Phys. Rev. Lett. 109, 167001 (2012).
Chang, J. et al. Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67 . Nat. Phys. 8, 871–876 (2012).
Blanco-Canosa, S. et al. Resonant X-ray scattering study of charge-density wave correlations in YBa2Cu3O6+x . Phys. Rev. B 90, 054513 (2014).
Tabis, W. et al. Charge order and its connection with Fermi-liquid charge transport in a pristine high-Tc cuprate. Nat. Commun. 5, 5875 (2014).
da Silva Neto, E. H. et al. Charge ordering in the electron-doped superconductor Nd2xCexCuO4 . Science 347, 282–285 (2015).
Comin, R. et al. Broken translational and rotational symmetry via charge stripe order in underdoped YBa2Cu3O6+y . Science 347, 1335–1339 (2015).
Comin, R. et al. Charge order driven by Fermi-arc instability in Bi2Sr2−xLaxCuO6+δ . Science 343, 390–392 (2014).
da Silva Neto, E. H. et al. Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates. Science 343, 393–396 (2014).
Wu, T. et al. Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy . Nat. Commun. 6, 6438 (2015).
v. Zimmermann, M. et al. Hard X-ray diffraction study of charge stripe order in La1.48Nd0.4Sr0.12CuO4 . Europhys. Lett. 41, 629–634 (1998).
Hinkov, V. et al. Spin dynamics in the pseudogap state of a high-temperature superconductor. Nat. Phys. 3, 780–785 (2007).
Tranquada, J. M. et al. Evidence for unusual superconducting correlations coexisting with stripe order in La1.875Ba0.125CuO4 . Phys. Rev. B 78, 174529 (2008).
Lawler, M. J. et al. Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states. Nature 466, 347–351 (2010).
Li, Y. et al. Hidden magnetic excitation in the pseudogap phase of a high-Tc superconductor. Nature 468, 283–285 (2010).
Karapetyan, H. et al. Magneto-optical measurements of a cascade of transitions in superconducting La1.875Ba0.125CuO4 single crystals. Phys. Rev. Lett. 109, 147001 (2012).
Sordi, G., Haule, K. & Tremblay, A.-M. S. Mott physics and first-order transition between two metals in the normal-state phase diagram of the two-dimensional Hubbard model. Phys. Rev. B 84, 075161 (2011).
Phillips, P. Normal state of the copper oxide high-temperature superconductors. Phil. Trans. R. Soc. A 369, 1572–1573 (2011).
Uchida, S. et al. Optical spectra of La2−xSrxCuO4: effect of carrier doping on the electronic structure of the CuO2 plane. Phys. Rev. B 43, 7942–7954 (1991).
Lupi, S. et al. Far-infrared absorption and the metal-to-insulator transition in hole-doped cuprates. Phys. Rev. Lett. 102, 206409 (2009).
Nicoletti, D. et al. High-temperature optical spectral weight and Fermi-liquid renormalization in bi-based cuprate superconductors. Phys. Rev. Lett. 105, 077002 (2010).
Dal Conte, S. et al. Disentangling the electronic and phononic glue in a high-Tc superconductor. Science 335, 1600–1603 (2012).
Dal Conte, S. et al. Snapshots of the retarded interaction of charge carriers with ultrafast fluctuations in cuprates. Nat. Phys. 11, 421–426 (2015).
Hansmann, P., Parragh, N., Toschi, A., Sangiovanni, G. & Held, K. Importance of d–p Coulomb interaction for high Tc cuprates and other oxides. New J. Phys. 16, 033009 (2014).
Falck, J. P., Levy, A., Kastner, M. A. & Birgeneau, R. J. Charge-transfer spectrum and its temperature dependence in La2CuO4 . Phys. Rev. Lett. 69, 1109–1112 (1992).
Novelli, F. et al. Witnessing the formation and relaxation of dressed quasi-particles in a strongly correlated electron system. Nat. Commun. 5, 5112 (2014).
Kawasaki, S., Lin, C., Kuhns, P. L., Reyes, A. P. & Zheng, G.-q. Carrier-concentration dependence of the pseudogap ground state of superconducting Bi2Sr2−xLaxCuO6+δ revealed by 63,65Cu-nuclear magnetic resonance in very high magnetic fields. Phys. Rev. Lett. 105, 137002 (2010).
Cilento, F. et al. Photo-enhanced antinodal conductivity in the pseudogap state of high-Tc cuprates. Nat. Commun. 5, 4353 (2014).
Grilli, M., Raimondi, R., Castellani, C., Di Castro, C. & Kotliar, G. Superconductivity, phase separation, and charge-transfer instability in the U = ∞ limit of the three-band model of the CuO2 planes. Phys. Rev. Lett. 67, 259–262 (1991).
Sordi, G., Sémon, P., Haule, K. & Tremblay, A.-M. S. Pseudogap temperature as a Widom line in doped Mott insulators. Sci. Rep. 2, 547 (2012).
Fisher, D., Kotliar, G. & Moeller, G. Midgap states in doped Mott insulators in infinite dimensions. Phys. Rev. B 52, 17112–17118 (1995).
Fujita, K. et al. Simultaneous transitions in cuprate momentum-space topology and electronic symmetry breaking. Science 344, 612–616 (2014).
He, Y. et al. Fermi surface and pseudogap evolution in a cuprate superconductor. Science 344, 608–611 (2014).
Fournier, D. et al. Loss of nodal quasiparticle integrity in underdoped YBa2Cu3O6+x . Nat. Phys. 6, 905–911 (2010).
Deutscher, G., Santander-Syro, A. F. & Bontemps, N. Kinetic energy change with doping upon superfluid condensation in high-temperature superconductors. Phys. Rev. B 72, 092504 (2005).
Giannetti, C. et al. Revealing the high-energy electronic excitations underlying the onset of high-temperature superconductivity in cuprates. Nat. Commun. 2, 353 (2011).
Xia, J. et al. Polar Kerr-effect measurements of the high-temperature YBa2Cu3O6+x superconductor: evidence for broken symmetry near the pseudogap temperature. Phys. Rev. Lett. 100, 127002 (2008).
Ando, Y., Komiya, S., Segawa, K., Ono, S. & Kurita, Y. Electronic phase diagram of high-Tc cuprate superconductors from a mapping of the in-plane resistivity curvature. Phys. Rev. Lett. 93, 267001 (2004).
Ono, S. et al. Metal-to-insulator crossover in the low-temperature normal state of Bi2Sr2−xLaxCuO6+δ . Phys. Rev. Lett. 85, 638–641 (2000).
Badoux, S. et al. Change of carrier density at the pseudogap critical point of a cuprate superconductor. Nature 531, 210–214 (2016).
Laliberté, F. et al. Origin of the metal-to-insulator crossover in cuprate superconductors. Preprint at http://arXiv.org/abs/1606.04491 (2016).
Ramshaw, B. J. et al. Quasiparticle mass enhancement approaching optimal doping in a high-tc superconductor. Science 348, 317–320 (2015).
Ando, Y. et al. Carrier concentrations in Bi2Sr2−zLazCu6+δ single crystals and their relation to the Hall coefficient and thermopower. Phys. Rev. B 61, R14956–R14959 (2000).
Ono, S. & Ando, Y. Evolution of the resistivity anisotropy in Bi2Sr2−xLaxCuO6+δ single crystals for a wide range of hole doping. Phys. Rev. B 67, 104512 (2003).
We thank M. Grilli, A. Bianconi, L. Benfatto, F. Cilento, D. Fausti, F. Parmigiani, L. De’ Medici, M. Minola, B. Keimer and J. Bonča for useful and fruitful discussions. The research activities of M.F. have received funding from the European Union, under the project ERC-692670 (FIRSTORM). F.B. acknowledges financial support from the MIUR-Futuro in ricerca 2013 Grant in the frame of the ULTRANANO Project (project number: RBFR13NEA4). M.C. and C.G. acknowledge financial support from MIUR through the PRIN 2015 Programme (Prot. 2015C5SEJJ001). M.C. acknowledges funding by SISSA/CNR project ‘Superconductivity, Ferroelectricity and Magnetism in Bad Metals’ (Prot. 232/2015). F.B., G.F. and C.G. acknowledge support from Università Cattolica del Sacro Cuore through D.1, D.2.2 and D.3.1 grants. F.B. and G.F. acknowledge financial support from Fondazione E.U.L.O. D.B. acknowledges the Emmy Noether Programme of the Deutsche Forschung Gemeinschaft. G.C. acknowledges funding from the European Union Horizon 2020 Programme under Grant Agreement 696656 Graphene Core 1. This research was undertaken thanks in part to funding from the Max Planck-UBC Centre for Quantum Materials and the Canada First Research Excellence Fund, Quantum Materials and Future Technologies Program. The work at UBC was supported by the Killam, Alfred P. Sloan, and Natural Sciences and Engineering Research Council of Canada’s (NSERC’s) Steacie Memorial Fellowships (A.D.); the Alexander von Humboldt Fellowship (A.D.); the Canada Research Chairs Program (A.D.); and the NSERC, Canada Foundation for Innovation (CFI), and CIFAR Quantum Materials.
The authors declare no competing financial interests.
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Peli, S., Conte, S., Comin, R. et al. Mottness at finite doping and charge instabilities in cuprates. Nature Phys 13, 806–811 (2017). https://doi.org/10.1038/nphys4112
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