The cuprates exhibit a prominent charge-density-wave (CDW) instability with a wave vector along , i.e., the Cu-O bond direction. Whereas CDW order is most prominent at moderate doping and low temperature, there exists increasing evidence for dynamic charge correlations throughout a large portion of the temperature-doping phase diagram. In particular, the signatures of incipient charge order have been observed as phonon softening and/or broadening near the CDW wave vector approximately halfway through the Brillouin zone. Most of this work is focused on moderately doped cuprates, for which the CDW order is robust, or on optimally doped samples, for which the superconducting transition temperature (Tc) attains its maximum. Here we present a time-of-flight neutron scattering study of phonons in simple-tetragonal HgBa2CuO4+δ(Tc=55K) at a low doping level where prior work showed the CDW order to be weak. We employ and showcase a new software-based technique that mines a large number of measured Brillouin zones for useful data in order to improve accuracy and counting statistics. Density-functional theory has not provided an accurate description of phonons in HgBa2CuO4+δ, yet we find the right set of parameters to qualitatively reproduce the data. The notable exception is a dispersion minimum in the longitudinal Cu-O bond-stretching branch along . This discrepancy suggests that, while CDW order is weak, there exist significant dynamic charge correlations in the optic phonon range at low doping, near the edge of the superconducting dome.
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We thank M. K. Chan, Y. Tang, and G. Yu for their help with sample preparation and R. Heid for helpful discussions and preliminary DFT calculations. The work at the University of Colorado was supported by the DOE, Office of Basic Energy Sciences, Office of Science, under Contract No. DE-SC0006939. The work at the University of Minnesota was funded by the Department of Energy through the University of Minnesota Center for Quantum Materials under DE-SC-0016371. This research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory.