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The infinite-layer cuprate $A$CuO$_2$ ($A=$ Ca, Sr, Ba) has the simplestcrystal structure among numerous cuprate superconductors and can serve aprototypical system to explore the unconventional superconductivity. Based onthe first-principles electronic structure calculations, we have studied theelectronic and magnetic properties of the infinite-layer cuprate SrCuO$_{2}$from a phonon perspective. We find that interesting fluctuations of charges,electrical dipoles, and local magnetic moments can be induced by the zero-pointvibrations of phonon modes in SrCuO$_{2}$ upon the hole doping. Among alloptical phonon modes of SrCuO$_{2}$ in the antiferromagnetic N\'{e}el state,only the $A_{1}$$_g$ mode that involves the full-breathing O vibrations alongthe Cu-O bonds can cause significant fluctuations of local magnetic moments onO atoms and dramatic charge redistributions between Cu and O atoms. Notably,due to the zero-point vibration of the $A_{1g}$ mode, both the chargefluctuations on Cu and the electrical dipoles on O show a dome-like evolutionwith increasing hole doping, quite similar to the experimentally observedbehavior of the superconducting $T_c$; in comparison, the fluctuations of localmagnetic moments on O display a monotonic enhancement along with the holedoping. Further analyses indicate that around the optimal doping, there exist alarge softening in the frequency of the $A_{1g}$ phonon mode and a van Hovesingularity in the electronic structure close to the Fermi level, suggestingpotential electron-phonon coupling. Our work reveals the important role of thefull-breathing O phonon mode playing in the infinite-layer SrCuO$_{2}$, whichmay provide new insights in understanding the cuprate superconductivity.

Exploring charge and spin fluctuations in infinite-layer cuprate SrCuO$_{2}$ from a phonon perspective