Recently discovered superconducting infinite-layer nickelates $R{\mathrm{NiO}}_2$ ($R$=Nd, La, Pr) attracts increasing attention as a similar system to cuprates. Both $R{\mathrm{NiO}}_2$ and YBCO cuprates display the three-dimensional (3D) CDW with wave vector $\mathit{q}\sim (2\pi /3,0,q_z)$, while $q_z$ is nonzero and incommensurate in the former system. Here, we reveal that the characteristic CDW in $R{\mathrm{NiO}}_2$ can be explained as the quantum interference between paramagnons, by focusing on the following characteristics of $R{\mathrm{NiO}}_2$: (i) prominent three dimensionality in the Fermi surface and (ii) large self-hole doping ($\sim 14\%$). This mechanism predicts the emergence of the $d_{x^2-y^2}$-wave bond order at a secondary 3D nesting vector ${\mathit{q}}^c\sim (2\pi /3,0,q_z^c)(q_z^c=0.2\pi \sim 2\pi /3)$. The obtained strong bond fluctuations lead to the non-Fermi liquid electronic states and superconducting states in nickelates.

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• Charge density waves
• Nickelates
• Strongly correlated systems