  Using density functional theory calculations including a Hubbard $U$ term we
explore the effect of strain and confinement on the electronic ground state of
superlattices containing the band insulator LaAlO$_3$ and the correlated metal
LaNiO$_3$. Besides a suppression of holes at the apical oxygen, a central
feature is the asymmetric response to strain in single unit cell superlattices:
For tensile strain a band gap opens due to charge disproportionation at the Ni
sites with two distinct magnetic moments of 1.45$\mu_{\rm B}$ and 0.71$\mu_{\rm
B}$. Under compressive stain, charge disproportionation is nearly quenched and
the band gap collapses due to overlap of $d_{3z^2-r^2}$ bands through a
semimetallic state. This asymmetry in the electronic behavior is associated
with the difference in octahedral distortions and rotations under tensile and
compressive strain. The ligand hole density and the metallic state are quickly
restored with increasing thickness of the (LaAlO$_3$)$_n$/(LaNiO$_3$)$_n$
superlattice from $n=1$ to $n=3$.
