Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate

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 order lock-in by electron-phonon coupling in La 1.675 Eu 0.2 Sr 0.125 CuO 4

“…Phase excitations of stripes couple to the lattice and create a splitting of the in-phase and out-of-phase oscillation modes (35). However, the phonon anomaly is expected (35) to exist within a narrow (17,19,20). This is supported by a nonmonotonically increasing phonon intensity versus momentum and an excitation energy softening that exceeds expectations for EPC.…”

“…By contrast, the here reported softening magnitude in LESCO is consistent with typical phononic self-energy effects ( 10 , 33 ). In addition, the intensity enhancement in the Bi-based compounds is more intense and leads to a dome-shaped h dependence ( 17 , 19 , 20 ), whereas in LESCO, the enhanced intensity is still smaller compared to that near the zone boundary ( Fig. 3D ).…”

“…Another notable effect of charge excitation is its Fano interference with intersecting optical phonons. Recent RIXS results on Bi-based cuprates Bi 2 Sr 2 CaCu 2 O 8+δ and Bi 2 Sr 2 LaCuO 6+δ are interpreted in terms of a Fano resonance between dispersive charge excitations and optical phonon modes ( 17 , 19 , 20 ). This is supported by a nonmonotonically increasing phonon intensity versus momentum and an excitation energy softening that exceeds expectations for EPC.…”

“…Recent advances of the resonant IXS (RIXS) technique have enabled studies of optical phonons, charge excitations, and their Fano interference (16)(17)(18)(19)(20)(21)(22). The RIXS phonon scattering cross section is directly proportional to the EPC strength (see Fig.…”

Charge Density Waves in YBa2Cu3O6.67 Probed by Resonant X-Ray Scattering under Uniaxial Com

“…Nevertheless, as they do affect the shape of the Fermi surface via hybridization between energy bands derived from the CuO 2 planes and the CuO chains, they may thus indirectly influence the propensity of the electron system in the CuO 2 planes to CDW formation. The importance of electron-phonon interactions (EPI) for the formation of the CDW in the cuprates has been highlighted [9,26,41,[46][47][48][49], and research on classical CDW compounds has shown that its momentum dependence is also a critical parameter [50][51][52]. We argue here that the pronounced a=b anisotropies of EPI for high-energy phonons reported in YBCO [53,54] reflect the influence of the CuO chains on the EPI and play an important role in destabilizing the 3D a-CDW relative to the b-CDW.…”