Hybrid functional calculations for the electronic properties of LaAlO$_3$*

The perovskite LaAlO$_3$ is a wide-band-gap (5.5--6.5 eV) insulator of high interest in both applied and fundamental research. On the applied side, LaAlO$_3$ has been considered a candidate to replace SiO$_2$ as a gate dielectric in field-effect transistors due to its high dielectric constant (23--25) and near-perfect lattice matching with Si ($<1$\%). On the fundamental science side, two-dimensional electron gases (2DEGs) with high carrier density have been observed at the interface of LaAlO$_3$ and SrTiO$_3$. The origin of the 2DEG and the dependency of its density on the thickness of the LaAlO$_3$ top layer have been highly debated. Interestingly, many of the basic electronic properties of LaAlO$_3$ are still poorly understood. For example, measurements of the band gap vary by as much as 1 eV. Here, we report the electronic structure of LaAlO$_3$ using density functional calculations with a hybrid functional. We compute the electronic structure and the dielectric function of bulk LaAlO$_3$ in the rhombohedral and cubic phases, and compare the optical properties with experiments.