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 ${\bf q}\sim(2\pi/3,0,q_z)$, 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 ${\bf q}^c\sim(2\pi/3,0,q^c_z)$ $(q^c_z=0.2\pi\sim 2\pi/3)$. The obtained strong bond fluctuations lead to the non-Fermi liquid electronic states and superconducting states in nickelates.