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

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 loosely bound oxygens leaves behind voids with a landscape of attractive potentials for electrons. We show that this is also what happens in the IL nickelates, where one of the two electrons (per formula unit) freed during the topotactic synthesis is to a large degree located in the oxygen vacancy position, occupying partially a local $s$-symmetry interstitial orbital, rather than taking 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 covalent bonds with neighboring Ni $3d_{3z^2-r^2}$ orbitals, which in turn facilitates the 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 coupling between Ni magnetic moments. This finding, reinforced by our electron localization function analysis, points to a fundamental distinction between the nickelates and the structurally analogous cuprates, may explain the absence of superconductivity in hydrogen-poor samples, and is certainly in agreement with the observed large $z$-polarized component in the Ni $L_3$-edge x-ray absorption spectra. In addition, by using DFT+U calculations as an illustration, we show that the electride-like nature of the IL nickelates is one of the main reasons for the theoretical difficulty in determining the much debated elusive Fermi surface of these novel superconductors and aslo in exploring the possibility of them becoming excitonic insulators at low temperatures.