We present a detailed synchrotron x-ray scattering study of the charge-density-wave (CDW) order in simple tetragonal HgBa2CuO4+δ (Hg1201). Resonant soft x-ray scattering measurements reveal that short-range order appears at a temperature that is distinctly lower than the pseudogap temperature and in excellent agreement with a prior transient reflectivity result. Despite considerable structural differences between Hg1201 and YBa2Cu3O6+δ, the CDW correlations exhibit similar doping dependencies, and we demonstrate a universal relationship between the CDW wave vector and the size of the reconstructed Fermi pocket observed in quantum oscillation experiments. The CDW correlations in Hg1201 vanish already below optimal doping, once the correlation length is comparable to the CDW modulation period, and they appear to be limited by the disorder potential from unit cells hosting two interstitial oxygen atoms. A complementary hard x-ray diffraction measurement, performed on an underdoped Hg1201 sample in magnetic fields along the crystallographic c axis of up to 16 T, provides information on the form factor of the CDW order. As expected from the single-CuO2-layer structure of Hg1201, the CDW correlations vanish at half-integer values of L and appear to be peaked at integer L. We conclude that the atomic displacements associated with the short-range CDW order are mainly planar, within the CuO2 layers.
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We thank A. V. Chubukov, M.-H. Julien, Y. Li, E. H. da Silva Neto, and C. Proust for valuable comments on the manuscript, and acknowledge the contributions of M. K. Chan, C. J. Dorow, and M. J. Veit to the sample preparation. The work at the University of Minnesota (crystal growth and characterization, x-ray measurements and data analysis) was funded by the Department of Energy through the University of Minnesota Center for Quantum Materials, under DE-SC-0016371 and DE-SC-0006858. Research performed at the Canadian Light Source was supported by CFI, NSERC, the University of Saskatchewan, the Government of Saskatchewan, Western Economic Diversification Canada, NRC, and CIHR. Work at HASYLAB and TUW was supported by FWF Project No. P27980-N36. Work with the Birmingham 17 T cryomagnet was supported by the UK EPSRC, Grant No. EP/J016977/1. E.M.F. was supported by the Leverhulme Foundation. The data were analyzed using the SPECPLOT and SPCFIT packages ( http://webusers.spa.umn.edu/~yu/index.html ).