Orbital Order and Possible Superconductivity in ${\mathrm{LaNiO}}_3/{\mathrm{LaMO}}_3$ Superlattices

A hypothetical layered oxide ${\mathrm{La}}_2\mathrm{Ni}M{\mathrm{O}}_6$ where ${\mathrm{NiO}}_2$ and $M{\mathrm{O}}_2$ planes alternate along the $c$ axis of $AB{\mathrm{O}}_3$ perovskite lattice is considered theoretically. Here, $M$ denotes a trivalent cation Al, Ga,… such that $M{\mathrm{O}}_2$ planes are insulating and suppress the $c$-axis charge transfer. We predict that correlated $e_g$ electrons in the ${\mathrm{NiO}}_2$ planes develop a planar $x^2\mathrm{\text{−}}{y}^2$ orbital order driven by the reduced dimensionality and further supported by epitaxial strain from the substrate. Low-energy electronic states can be mapped to a single-band $t-t^{\prime }-J$ model, suggesting favorable conditions for high-$T_c$ superconductivity.

Figure 1

(a) Superlattice ${\mathrm{La}}_2\mathrm{Ni}M{\mathrm{O}}_6$ with alternating ${\mathrm{NiO}}_2$ and $M{\mathrm{O}}_2$ planes. $M{\mathrm{O}}_2$ layers suppress the $c$-axis hopping resulting in 2D electronic structure. Arrows indicate the $c$-axis compression of the ${\mathrm{NiO}}_6$ octahedron imposed by tensile epitaxial strain and supported by Jahn-Teller coupling. (b) ,(c), (d) Strain-induced stretching of the ${\mathrm{NiO}}_2$ planes occurs when superlattices with $M=\mathrm{Al}$, Ga, Ti are grown on ${\mathrm{SrTiO}}_3$ or ${\mathrm{LaGaO}}_3$ substrates having large lattice parameter compared to that of ${\mathrm{LaNiO}}_3$. Expected deformations are indicated by arrows.

Figure 2

Phase diagram of the spin-orbital Hamiltonian (2). The $c$-axis hopping is $0.3t_0$. The labels $AAA$, etc., indicate the magnetic order, with $F$ ($A$) denoting parallel (antiparallel) orientations of the NN spins in the $a$, $b$, and $c$ directions. Representative orbital states are sketched. In the pure planar-orbital phase (left-bottom), a weak $A$ coupling between the layers is due to the higher order hoppings. Upper right panel: the phase diagram for $\Delta ={ϵ}_z-{ϵ}_x=0.5J_0$, the gray area indicates the planar-orbital spin-$AAA$ phase. Lower right panel: the phase diagram at 5% hole doping ($\Delta =0$, $J=0.3t_0$) shows that charge carriers strongly favor the planar-orbital phase.

Figure 3

The band structure and density of states for the $e_g$ orbital splitting ${ϵ}_z-{ϵ}_x=0.25t_0$ at doping levels (a) 100% (bare bands), (b) 20%, and (c) 5%. The dotted curves show the density of states projected onto the $3z^2-r^2$ orbital. The gray areas indicate the occupied states at given $\delta$.

Figure 4

(a) The correlation-induced correction to the orbital splitting, and (b) the effective $t^{\prime }/t$ as function of doping $\delta$ for different ${ϵ}_z-{ϵ}_x$. (c) The mean-field $T_c$ [21] at various levels of $e_g$ orbital splitting. The dashed-dotted line (${ϵ}_z-{ϵ}_x=5t_0$) corresponds to the “cuprate” situation with inactive $3z^2-r^2$ state.