Molecular correlated insulating state in low-valence layered nickelates

In recent years, there has been an effort on artificially creating Fermi surfaces that resemble those of the superconducting cuprates. A Ni$^{3+}$:d$^7$ (one e$_g$ electron) configuration can be made into the electron-like analog of the d$^9$ (one e$_g$ hole) cuprate electronic structure.[1] Another cleaner alternative would be to grow low-valence Ni$^+$:d$^9$ compounds, which have recently become available through synthesis[2] of members of the series La$_{n+1}$Ni$_{n}$O$_{2n+2}$. We present LDA+U calculations on the layered compounds La$_4$Ni$_3$O$_8$ [3] and La$_3$Ni$_2$O$_6$, with three and two NiO$_2$ layers, respectively. Electron count implies very low Ni formal valencies: 1.33+ and 1.5+, respectively. If charge order is present, Ni$^+$:d$^9$ could occur in a geometry similar to that of the cuprates. However, this is not the case. Both compounds are insulators, which we can attribute to quantum confinement in the NiO$_2$ tri/bi-layers. The only states close to the Fermi level are Ni d$_{3z^2-r^2}$, which couple along the c-axis (Ni trimers or dimers). The insulating behavior must be viewed from a molecular orbital viewpoint, after AFM order within layers has narrowed the bands. Insulating behavior is that of a ``molecular" Mott insulator rather than a charge-ordered insulator. \newline [1] J. Chaloupka and G. Khaliullin, \emph{PRL} \textbf{100}, 016404 (2008). \newline [2] V. V. Poltavets \textsl{et al.}, \emph{Phys. Rev. Lett.} \textbf{102}, 046405 (2009). \newline [3] V. Pardo and W.E. Pickett, arXiv:1008.2707.