  The unconventional normal-state properties of the cuprates are often
discussed in terms of emergent electronic order that onsets below a putative
critical doping of xc = 0.19. Charge-density wave (CDW) correlations represent
one such order; however, experimental evidence for such order generally spans a
limited range of doping that falls short of the critical value xc, leading to
questions regarding its essential relevance. Here, we use x-ray diffraction to
demonstrate that CDW correlations in La2-xSrxCuO4 persist up to a doping of at
least x = 0.21. The correlations show strong changes through the
superconducting transition, but no obvious discontinuity through xc = 0.19,
despite changes in Fermi surface topology and electronic transport at this
doping. These results demonstrate the interaction between CDWs and
superconductivity even in overdoped cuprates and prompt a reconsideration of
the role of CDW correlations in the high-temperature cuprate phase diagram.
