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A description of phonon dynamics and charge response of the $n$-dopedhigh-temperature superconductor (HTSC) NdCuO is presented based upon amicroscopic modeling of the electronic density response. This is accomplishedstarting from the insulating state via the underdoped strange metallic to themore conventional metallic state by consecutive orbital selectiveincompressibility-compressibility transitions in terms of strict sum rules forthe charge response. The approach proposed in this work for the $n$-dopedHTSC's modifies the modeling recently applied to the $p$-doped compounds andexpresses an electron-hole asymmetry introduced by doping. A qualitativephysical picture consistent with our modeling of the electronic state in thecuprates is given in which a sufficiently broad set of orbital degrees offreedom, i.e. Cu3d/$4s$ and O$2p$ is essential. Within the framework of linearresponse theory we calculate full phonon dispersion curves in the differentphases. In particular, the strongly doping dependent anomalous high-frequencyoxygen bond-stretching modes (OBSM) found experimentally in the $p$-dopedHTSC's and also recently for $n$-doped Nd$_{1.85}$Ce$_{0.15}$CuO$_{4}$ areinvestigated and compared with experimental results from inelastic neutronscattering and inelastic x-ray scattering, respectively. We calculate ananticrossing scenario for the OBSM in $n$-doped NdCuO which is absent in thecase of $p$-doped LaCuO and relate it to the different crystal structure.Phonon-induced electronic charge redistributions of the anomalous OBSM due tononlocal electron-phonon interaction effects of charge-fluctuation type givingreason to dynamic stripes are also studied.

A microscopic modeling of phonon dynamics and charge response in NdCuO