Pressure induced spin-charge correlation in trilayer nickelate superconductors La₄Ni₃O₁₀

Trilayer La₄Ni₃O₁₀ has been recently found to develop superconductivity in its high-pressure phase, similar to the previously discovered bilayer La₃Ni₂O₇, but with a much lower transition temperature. An immediate question is the qualitative change of electronic correlations at high pressure, and their distinction from those in La₃Ni₂O₇, particularly concerning the unconventional superconductivity. Here, based on a multi-energy-scale derivation of the inter-layer dynamics, we study the dominant emergent spin-charge correlations and compare them with the bilayered La₃Ni₂O₇. Similar to the latter, we find fractionalization of ionic spin in the high-pressure phase that drives the observed first-order structural transition. This results in a low-energy effective description resembling that of the cuprates and La₃Ni₂O₇, suggesting a similar microscopic mechanism of unconventional superconductivity and its corresponding properties. Furthermore, in contrast to La₃Ni₂O₇, the relative enhancement of the inter-layer spin-correlation offers a natural explanation for the significant weakening of superconductivity in this new family of unconventional superconductors.