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

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 with wave vector $\mathbf{q}\sim (2\pi \mathrm{/}3,0,q_z)$, while $q_z$ is non-zero and incommensurate in the former system. Here, we reveal that the characteristic CDW in $R$NiO${}_2$ can be naturally explained as the quantum interference between 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 of the $d_{x^2-y^2}$-wave bond order at a secondary 3D nesting vector ${\mathbf{q}}^c\sim (2\pi \mathrm{/}3,0,q_z^c)$ $(q_z^c=0.2\pi \sim 2\pi \mathrm{/}3)$. The obtained strong bond fluctuations lead to the non-Fermi liquid electronic states and superconducting states in nickelates.