Researchers propose a microscopic mechanism that links unusual charge order and high-temperature superconductivity in the trilayer nickelate La4Ni3O10. They show that quantum interference between short-range spin fluctuations can create a bond pattern between the outer nickel-oxide layers. That bond pattern appears at a wavevector about twice the spin-wavevector, matching a key experimental relation Q_cdw ≈ 2 Q_sdw seen in experiments.

To reach this result the authors built a realistic six-band model of the trilayer crystal. The model includes the two nickel orbitals that dominate low-energy behavior on each of the three NiO2 layers. They treated electronic correlations with a fluctuation-exchange (FLEX) approximation and then solved a density-wave equation that includes Aslamazov–Larkin vertex corrections. Those vertex corrections capture quantum interference between paramagnons, which are collective spin fluctuations that exist even without long-range magnetic order.

Their calculations find that the leading spin fluctuations live mainly on the two outer layers and have opposite sign on those layers (an odd parity under mirror exchange). Quantum interference between such outer-layer spin fluctuations generates an inter-outer-layer bond order at the charge wavevector Q_cdw ≈ 2 Q_sdw. That bond order then forces a strong orbital pattern in the inner layer: the occupations of the Ni d_{3z^2−r^2} and d_{x^2−y^2} orbitals modulate out of phase, producing large orbital polarization but only a weak net change in total charge on each site.

This intertwined bond-and-orbital order helps to explain several experimental observations. NMR and NQR experiments report a layer-selective electronic reconstruction, with the inner layer showing a charge-related anomaly before long-range spin order sets in. Polarized Raman spectroscopy and scanning-tunnelling microscopy (STM) also indicate multiorbital and unidirectional charge features that are consistent with the predicted pattern. The paper also points out a symmetry link to superconductivity: the charge form factor is even under mirror symmetry about the inner layer while the spin form factor is odd. Those mirror-parity selection rules let the same fluctuations cooperate to stabilize an s_{±}-wave superconducting state, a sign-changing form of s-wave pairing.