Pressure-induced trans-proximate correlation in La${}_4$Ni${}_3$O${}_{10}$ and possible routes to enhance its superconductivity

We report an unexpected trans-proximate interlayer correlation (stronger correlation between disjoint layers than the adjacent ones) in the high-pressure phase of the recently discovered La${}_4$Ni${}_3$O${}_{10}$ superconductors. Accompanied by an unusual pressure-induced fractionalization of Ni${}^{2+}$ ionic spin from the standard spin-1 to spin-$\frac{1}{2}$, this trans-proximate correlation results from the emergence of a cross-layer trimer in our multi-energy-scale derivation of the electron dynamics. The resulting low-energy effective description resembles that of the cuprates and suggests a universal superconducting mechanism in all existing nickelate and cuprate superconductors. The rare trans-proximate correlation not only explains the weaker superconductivity in comparison with the related La${}_3$Ni${}_2$O${}_7$ samples, but it also indicates a viable strategy to improve superconductivity in this trilayer nickelate by lowering layer symmetry. Such pressure-induced trans-proximate correlation is expected in many materials and examplifies the engineering of rich uncharted quantum states of matter through pressure.