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

Three-dimensional bond-order instability in infinite-layer nickelates due to nonlocal quantum interference