No abstract

Copper oxide high-T C superconductors possess a number of exotic orders that coexist with or are proximal to superconductivity. Quantum fluctuations associated with these orders may account for the unusual characteristics of the normal state, and possibly affect the superconductivity 1-4 . Yet, spectroscopic evidence for such quantum fluctuations remains elusive. Here, we use resonant inelastic X-ray scattering to reveal spectroscopic evidence of fluctuations associated with a charge order 5-14 in nearly optimally doped Bi 2 Sr 2 CaCu 2 O 8+δ . In the superconducting state, while the quasielastic charge order signal decreases with temperature, the interplay between charge order fluctuations and bond-stretching phonons in the form of a Fano-like interference increases, an observation that is incompatible with expectations for competing orders. Invoking general principles, we argue that this behaviour reflects the properties of a dissipative system near an orderdisorder quantum critical point, where the dissipation varies with the opening of the pseudogap and superconducting gap at low temperatures, leading to the proliferation of quantum critical fluctuations, which melt charge order.Charge order (CO), which is ubiquitous in hole-doped cuprates [5][6][7][8][9][10][11][12][13][14] , is accompanied by a negligible lattice deformation (approximately 0.1 pm, ref. 15 ); however, signatures of valence electron density modulations due to CO can be detected by resonant inelastic X-ray scattering (RIXS) at the Cu L edge. RIXS resolves both the quasistatic and dynamical inelastic signals 8,16 , as highlighted in Fig. 1a, particularly the intensity of the inelastic branch of excitations below 0.1 eV. These excitations possess an energy scale similar to that of bond-stretching phonons, which exhibit anomalous softening and broadening in certain portions of reciprocal space, observed using inelastic neutron scattering and non-resonant inelastic X-ray scattering 17,18 . These behaviours have suggested a coupling with CO 17,18 and possibly some form of charge collective mode 19 . However, while neutron and non-resonant X-ray scattering measure the phonon self-energy (meaning the dynamical structure factor), RIXS largely reflects the electron-phonon coupling itself and its interplay with charge excitations 16,20 . With superb momentum resolution, RIXS at the Cu L edge has already revealed two distinct anomalies associated with CO excitations due to a Fano-like interference effect 16 , as shown in Fig. 1b: (1) an apparent softening of the RIXS phonon at the CO wave-vector (Q CO ), and (2) creation of a 'funnel'-like spectral weight emanating from Q CO with a

Charge-density waves (CDWs) are ubiquitous in underdoped cuprate superconductors. As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3dand O-2porbital character owing to the strong hybridization of these orbitals near the Fermi level. Here, we investigate underdoped Bi2Sr1.4La0.6CuO6+δusing resonant inelastic X-ray scattering (RIXS) and find that a short-range CDW exists at both Cu and O sublattices in the copper-oxide (CuO2) planes with a comparable periodicity and correlation length. Furthermore, we uncover bond-stretching and bond-buckling phonon anomalies concomitant to the CDWs. Comparing to slightly overdoped Bi2Sr1.8La0.2CuO6+δ, where neither CDWs nor phonon anomalies appear, we highlight that a sharp intensity anomaly is induced in the proximity of the CDW wavevector (QCDW) for the bond-buckling phonon, in concert with the diffused intensity enhancement of the bond-stretching phonon at wavevectors much greater than QCDW. Our results provide a comprehensive picture of the quasistatic CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates.