Visualizing the evolution from the Mott insulator to a charge-ordered insulator in lightly doped cuprates

Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).

Timusk, T. & Statt, B. The pseudogap in high-temperature superconductors: an experimental survey. Rep. Prog. Phys. 62, 61–122 (1999).

Fischer, Ø., Kugler, M., Maggio-Aprile, I., Berthod, C. & Renner, C. Scanning tunneling spectroscopy of high-temperature superconductors. Rev. Mod. Phys. 79, 353–419 (2007).

Hashimoto, M., Vishik, I. M., He, R.-H., Devereaux, T. P. & Shen, Z.-X. Energy gaps in high-transition-temperature cuprate superconductors. Nature Phys. 10, 483–495 (2014).

Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987).

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).

Hoffman, J. E. et al. A four unit cell periodic pattern of quasi-particle states surrounding vortex cores in Bi2Sr2CaCu2O8+δ . Science 295, 466–469 (2002).

Hanaguri, T. et al. A /‘checkerboard/’ electronic crystal state in lightly hole-doped Ca2−xNaxCuO2Cl2 . Nature 430, 1001–1005 (2004).

Vershinin, M. et al. Local ordering in the pseudogap state of the high-Tc superconductor Bi2Sr2CaCu2O8+δ . Science 303, 1995–1998 (2004).

Ghiringhelli, G. et al. Long-range incommensurate charge fluctuations in (Y, Nd)Ba2Cu3O6+x . Science 337, 821–825 (2012).

Comin, R. et al. Charge order driven by Fermi-arc instability in Bi2Sr2−xLaxCuO6+δ . Science 343, 390–392 (2014).

Aeppli, G., Mason, T. E., Hayden, S. M., Mook, H. A. & Kulda, J. Nearly singular magnetic fluctuations in the normal state of a high-Tc cuprate superconductor. Science 278, 1432–1435 (1997).

Lake, B. et al. Spins in the vortices of a high-temperature superconductor. Science 291, 1759–1762 (2001).

Hücker, M. et al. Competing charge, spin, and superconducting orders in underdoped YBa2Cu3Oy . Phys. Rev. B 90, 054514 (2014).

da Silva Neto, E. H. et al. Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates. Science 343, 393–396 (2014).

Chang, J. et al. Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67 . Nature Phys. 8, 871–876 (2012).

Kohsaka, Y. et al. Visualization of the emergence of the pseudogap state and the evolution to superconductivity in a lightly hole-doped Mott insulator. Nature Phys. 8, 534–538 (2012).

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).

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).

Peng, Y. et al. Disappearance of nodal gap across the insulator–superconductor transition in a copper-oxide superconductor. Nature Commun. 4, 2459 (2013).

Ye, C. et al. Visualizing the atomic-scale electronic structure of the Ca2CuO2Cl2 Mott insulator. Nature Commun. 4, 1365 (2013).

Wise, W. D. et al. Imaging nanoscale Fermi-surface variations in an inhomogeneous superconductor. Nature Phys. 5, 213–216 (2009).

Anderson, P. W. & Ong, N. P. Theory of asymmetric tunneling in the cuprate superconductors. J. Phys. Chem. Solids 67, 1–5 (2006).

Randeria, M., Sensarma, R., Trivedi, N. & Zhang, F.-C. Particle-hole asymmetry in doped Mott insulators: implications for tunneling and photoemission spectroscopies. Phys. Rev. Lett. 95, 137001 (2005).

Wise, W. D. et al. Charge-density-wave origin of cuprate checkerboard visualized by scanning tunnelling microscopy. Nature Phys. 4, 696–699 (2008).

Shen, K. M. et al. Nodal quasiparticles and antinodal charge ordering in Ca2−xNaxCuO2Cl2 . Science 307, 901–904 (2005).

He, R.-H. et al. From a single-band metal to a high-temperature superconductor via two thermal phase transitions. Science 331, 1579–1583 (2011).

Tabis, W. et al. Charge order and its connection with Fermi-liquid charge transport in a pristine high-Tc cuprate. Nature Commun. 5, 5875 (2014).

Raichle, M. et al. Highly anisotropic anomaly in the dispersion of the copper-oxygen bond-bending phonon in superconducting YBa2Cu3O7 from inelastic neutron scattering. Phys. Rev. Lett. 107, 177004 (2011).

Le Tacon, M. et al. Inelastic X-ray scattering in YBa2Cu3O6.6 reveals giant phonon anomalies and elastic central peak due to charge-density-wave formation. Nature Phys. 10, 52–58 (2014).

Chen, H.-D., Vafek, O., Yazdani, A. & Zhang, S.-C. Pair density wave in the pseudogap state of high temperature superconductors. Phys. Rev. Lett. 93, 187002 (2004).

Sebastian, S. E. et al. A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor. Nature 454, 200–203 (2008).

White, S. R. & Scalapino, D. J. Checkerboard patterns in the t-J model. Phys. Rev. B 70, 220506(R) (2004).