Identification of a characteristic doping for charge order phenomena in Bi-2212 cuprates via RIXS

Identifying quantum critical points (QCPs) and their associated fluctuations may hold the key to unraveling the unusual electronic phenomena observed in cuprate superconductors. Recently, signatures of quantum fluctuations associated with charge order (CO) have been inferred from the anomalous enhancement of CO excitations that accompany the reduction of the CO order parameter in the superconducting state. To gain more insight into the interplay between CO and superconductivity, here we investigate the doping dependence of this phenomenon throughout the Bi-2212 cuprate phase diagram using resonant inelastic x-ray scattering (RIXS) at the Cu L-3 edge. As doping increases, the CO wave vector decreases, saturating near a commensurate value of 0.25 reciprocal lattice unit beyond a characteristic doping p(c), where the correlation length becomes shorter than the apparent periodicity (4a(0)). Such behavior is indicative of the fluctuating nature of the CO; the proliferation of CO excitations in the superconducting state also appears strongest at p(c), consistent with expected behavior at a CO QCP. Intriguingly, p(c) appears to be near optimal doping, where the superconducting transition temperature T-c is maximal.