Fate of charge order in overdoped La-based cuprates

In high-temperature cuprate superconductors, stripe order refers broadly to a coupled spin and charge modulation with a commensuration of eight and four lattice units, respectively. How this stripe order evolves across optimal doping remains a controversial question. Here we present a systematic resonant inelastic x-ray scattering study of weak charge correlations in La2-xSrxCuO4 and La1.8-xEu0.2SrxCuO4. Ultra high energy resolution experiments demonstrate the importance of the separation of inelastic and elastic scattering processes. Long-range temperature-dependent stripe order is only found below optimal doping. At higher doping, short-range temperature-independent correlations are present up to the highest doping measured. This transformation is distinct from and preempts the pseudogap critical doping. We argue that the doping and temperature-independent short-range correlations originate from unresolved electron-phonon coupling that broadly peaks at the stripe ordering vector. In La2-xSrxCuO4, long-range static stripe order vanishes around optimal doping and we discuss both quantum critical and crossover scenarios.