Resonant x-ray scattering study of charge-density wave correlations in YBa${}_2$Cu${}_3$O${}_{6+x}$ under uniaxial stress

We report a comprehensive study of the uniaxial stress response of charge-density-wave (CDW) correlations in detwinned single crystals of the high temperature superconductor YBa${}_2$Cu${}_3$O${}_{6+x}$ (YBCO${}_{6+x}$) with $0.40\le x\le 0.93$ (hole-doping levels $0.072\le p\le 0.168$) by means of Cu $L_3$-edge resonant energy-integrated x-ray scattering (REXS). We show that the influence of uniaxial stress is strongly doping dependent: the quasi-two-dimensional CDW is enhanced by in-plane uniaxial stress in a wide hole doping range ($0.45\le x\le 0.80$), but only barely affected in the most underdoped and optimally doped samples ($x=0.40$ and 0.93), where the CDW correlation length is minimal. A stress-induced three-dimensionally long-range ordered (3D) CDW was observed only in YBCO${}_{6.50}$ and YBCO${}_{6.67}$. The temperature dependence of the 3D CDW clearly indicates a strong competition with superconductivity. Based on the systematic strain-, doping-, and temperature-dependent REXS measurements reported here, we discuss the relationship between charge order and superconductivity in YBCO${}_{6+x}$ and other cuprates.