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We demonstrate in this paper that the recently discovered infinite-layer (IL)nickelates have much in common with a class of materials known as electrides.Oxide based electrides are compounds in which topotactic removal of looselybound oxygens leaves behind voids with a landscape of attractive potentials forelectrons. We show that this is also what happens in the IL nickelates, whereone of the two electrons (per formula unit) freed during the topotacticsynthesis is to a large degree located in the oxygen vacancy position,occupying partially a local $s$-symmetry interstitial orbital, rather thantaking part alongside the other electon in converting Ni from 3+ to a full 1+oxidation state. We demonstrate that the interstitial orbital in question,referred to by us as the zeronium $s$ or Z $s$ orbital, forms strong covalentbonds with neighboring Ni $3d_{3z^2-r^2}$ orbitals, which in turn facilitatesthe one-dimensional-like dispersion of the Ni $3d_{3z^2-r^2}$ band along the$c$-axis direction, leading also to a possible large out-of-plane couplingbetween Ni magnetic moments. This finding, reinforced by our electronlocalization function analysis, points to a fundamental distinction between thenickelates and the structurally analogous cuprates, may explain the absence ofsuperconductivity in hydrogen-poor samples, and is certainly in agreement withthe observed large $z$-polarized component in the Ni $L_3$-edge x-rayabsorption spectra. In addition, by using DFT+U calculations as anillustration, we show that the electride-like nature of the IL nickelates isone of the main reasons for the theoretical difficulty in determining the muchdebated elusive Fermi surface of these novel superconductors and aslo inexploring the possibility of them becoming excitonic insulators at lowtemperatures.

Distinct electridelike nature of infinite-layer nickelates and the resulting theoretical challenges to calculate their electronic structure