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).
Tranquada, J. M., Sternlieb, B. J., Axe, J. D., Nakamura, Y. & Uchida, S. Evidence for stripe correlations of spins and holes in copper oxide superconductors. Nature 375, 561–563 (1995).
Fujita, M., Goka, H., Yamada, K. & Matsuda, M. Competition between charge- and spin-density-wave order and superconductivity in La1.875Ba0.125−xSrxCuO4. Phys. Rev. Lett. 88, 167008 (2002).
Abbamonte, P. et al. Spatially modulated ‘Mottness’ in La2-xBaxCuO4. Nat. Phys. 1, 155–158 (2005).
Wu, T. et al. Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy. Nature 477, 191–194 (2011).
Ghiringhelli, G. et al. Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O6+x. Science 337, 821–825 (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).
Gerber, S. et al. Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields. Science 350, 949–952 (2015).
Chang, J. et al. Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x. Nat. Commun. 7, 11494 (2016).
Tabis, W. et al. Charge order and its connection with Fermi-liquid charge transport in a pristine high-T
c cuprate. Nat. Commun. 5, 5875 (2014).
Hashimoto, M. et al. Direct observation of bulk charge modulations in optimally doped Bi1.5Pb0.6Sr1.54CaCu2O8+δ. Phys. Rev. B 89, 220511(R) (2014).
Comin, R. et al. Charge order driven by Fermi-arc instability in Bi2Sr2−
xLaxCuO6+δ. Science 343, 390–392 (2014).
Allais, A., Chowdhury, D. & Sachdev, S. Connecting high-field quantum oscillations to zero-field electron spectral functions in the underdoped cuprates. Nat. Commun. 5, 5771 (2014).
da Silva Neto, E. H. et al. Doping-dependent charge order correlations in electron-doped cuprates. Sci. Adv. 2, 1600782 (2016).
Tranquada, J. M. et al. Coexistence of, and competition between, superconductivity and charge-stripe order in La1.6−xNd0.4SrxCuO4. Phys. Rev. Lett. 78, 338–341 (1997).
Yamada, K. et al. Doping dependence of the spatially modulated dynamical spin correlations and the superconducting-transition temperature in La2−xSrxCuO4. Phys. Rev. B 57, 6165–6172 (1998).
Miao, H. et al. High-temperature charge density wave correlations in La1.875Ba0.125CuO4 without spin–charge locking. Proc. Natl Acad. Sci. USA 114, 12430 (2017).
Zanchi, D. & Schulz, H. J. Superconducting instabilities of the non-half-filled Hubbard model in two dimensions. Phys. Rev. B 54, 9509–9519 (1996).
Gonzalez, J. Charge instabilities near a van Hove singularity. Phys. Rev. B 63, 045114 (2001).
Holder, T. & Metzner, W. Incommensurate nematic fluctuations in two-dimensional metals. Phys. Rev. B 85, 165130 (2012).
Bulut, S., Atkinson, W. A. & Kampf, A. P. Spatially modulated electronic nematicity in the three-band model of cuprate superconductors. Phys. Rev. B 88, 155132 (2013).
King, D. M. et al. Observation of a saddle-point singularity in Bi2(Sr0.97Pr0.03)2CuO6+δ and its implications for normal and superconducting state properties. Phys. Rev. Lett. 73, 3298–3301 (1994).
Moretti Sala, M. et al. Energy and symmetry of dd excitations in undoped layered cuprates measured by Cu L3 resonant inelastic X-ray scattering. New J. Phys. 13, 043026 (2011).
Chen, C.-W., Choe, J. & Morosan, E. Charge density waves in strongly correlated electron systems. Rep. Prog. Phys. 79, 084505 (2016).
Comin, R. et al. Symmetry of charge order in cuprates. Nat. Mater. 14, 796–800 (2015).
Peng, Y. Y. et al. Direct observation of charge order in underdoped and optimally doped Bi2(Sr,La)2CuO6+δ by resonant inelastic X-ray scattering. Phys. Rev. B 94, 184511 (2016).
Braicovich, L. et al. The simultaneous measurement of energy and linear polarization of the scattered radiation in resonant inelastic soft X-ray scattering. Rev. Sci. Instrum. 85, 115104 (2014).
Ament, L. J. P., Ghiringhelli, G., Moretti Sala, M., Braicovich, L. & van den Brink, J. Theoretical demonstration of how the dispersion of magnetic excitations in cuprate compounds can be determined using resonant inelastic X-ray scattering. Phys. Rev. Lett. 103, 117003 (2009).
Abbamonte, P. Charge modulations versus strain waves in resonant X-ray scattering. Phys. Rev. B 74, 195113 (2006).
Kawasaki, S. J. et al. 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).
Croft, T. P., Lester, C., Senn, M. S., Bombardi, A. & Hayden, S. M. Charge density wave fluctuations in La2−xSrxCuO4 and their competition with superconductivity. Phys. Rev. B 89, 224513 (2014).
da Silva Neto, E. H. et al. Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates. Science 343, 393–396 (2014).
Tabis, W. et al. Synchrotron X-ray scattering study of charge-density-wave order in HgBa2CuO4+δ. Phys. Rev. B 96, 134510 (2017).
Campi, G. et al. Inhomogeneity of charge-density-wave order and quenched disorder in a high-T
c superconductor. Nature 525, 359–362 (2015).
Cai, P. et al. Visualizing the evolution from the Mott insulator to a charge-ordered insulator in lightly doped cuprates. Nat. Phys. 12, 1047–1052 (2016).
He, Y. et al. Fermi surface and pseudogap evolution in a cuprate superconductor. Science 344, 608–611 (2014).
Meng, J. Q. et al. Coexistence of Fermi arcs and Fermi pockets in a high-T
c copper oxide superconductor. Nature 462, 335–338 (2009).
Kondo, T. et al. Hole-concentration dependence of band structure in (Bi, Pb)2(Sr, La)2CuO6+δ determined by the angle-resolved photoemission spectroscopy. J. Electron Spectrosc. Relat. Phenom. 137, 663–668 (2004).
Emery, V. J. & Kivelson, S. A. 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).
Andergassen, S., Caprara, S., Di Castro, C. & Grilli, M. Anomalous isotopic effect near the charge ordering quantum criticality. Phys. Rev. Lett. 87, 056401 (2001).
Caprara, S., Di Castro, C., Seibold, G. & Grilli, M. Dynamical charge density waves rule the phase diagram of cuprates. Phys. Rev. B 95, 224511 (2017).
Metlitski, M. A. & Sachdev, S. Quantum phase transitions of metals in two spatial dimensions. II Spin density wave order. Phys. Rev. B 82, 075128 (2010).
Efetov, K. B., Meier, H. & Pépin, C. Pseudogap state near a quantum critical point. Nat. Phys. 9, 442–445 (2013).
Wang, Y. & Chubukov, A. Charge-density-wave order with momentum (2Q,0) and (0,2Q) within the spin-fermion model: Continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates. Phys. Rev. B 90, 035149 (2014).
Markiewicz, R. S. A survey of the van Hove scenario for high-T
c superconductivity with special emphasis on pseudogaps and striped phases. J. Phys. Chem. Sol. 58, 1179–1310 (1997).
Zhao, L. et al. High-quality large-sized single crystals of Pb-doped Bi2Sr2CuO6+δ high-T
c superconductors grown with traveling solvent floating zone method. Chin. Phys. Lett. 27, 087401 (2010).
Kotliar, G. & Ruckenstein, A. E. New functional integral approach to strongly correlated Fermi systems: The Gutzwiller approximation as a saddle point. Phys. Rev. Lett. 57, 1362–1365 (1986).