Manifest charge-transfer physics in T$^\prime$-La$_2$NiO$_4$

The La$_2$NiO$_4$ compound stabilizes in nature in the so-called T structure with octahedral oxygen coordination of the Ni site. Motivated by a similarly existing polymorph for La$_2$CuO$_4$ in the cuprate system, we here study La$_2$NiO$_4$ in the T$^\prime$-structure with square-planar oxygen coordination of Ni by means of first-principles many-body theory. The hypothetical T$^\prime$-La$_2$NiO$_4$ compound turns out to be a manifest charge-transfer insulator with a cuprate-like charge gap of $\sim 1.8$ eV. Upon doping, a strong carrier asymmetry is revealed, i.e. while holes dominantly enter O$(2p)$-derived states, electrons may become itinerant majorly within effective Ni-$d_{x^2-y^2}$ states. Nearest-neighbor antiferromagnetic ordering at stoichiometry appears absent in the T$^\prime$ structure, in stark contrast to the strong antiferromagnetism in the T structure. Our theoretical study opens up new pathways for correlation physics in layered nickelates with challenging charge-transfer signatures, awaiting experimental inquiries.