  We present a first-principles study of the electronic structures and
properties of ideal (atomically sharp) LaAlO3/SrTiO3 (001) heterointerfaces and
their variants such as a new class of quantum well systems. We demonstrate the
insulating-to-metallic transition as a function of the LaAlO3 film thickness in
these systems. After the phase transition, we find that conduction electrons
are bound to the n-type interface while holes diffuse away from the p-type
interface, and we explain this asymmetry in terms of a large hopping matrix
element that is unique to the n-type interface. We build a tight-binding model
based on these hopping matrix elements to illustrate how the conduction
electron gas is bound to the n-type interface. Based on the `polar catastrophe'
mechanism, we propose a new class of quantum wells at which we can manually
control the spatial extent of the conduction electron gas. In addition, we
develop a continuous model to unify the LaAlO3/SrTiO3 interfaces and quantum
wells and predict the thickness dependence of sheet carrier densities of these
systems. Finally, we study the external field effect on both LaAlO3/SrTiO3
interfaces and quantum well systems. Our systematic study of the electronic
reconstruction of LaAlO3/SrTiO3 interfaces may serve as a guide to engineering
transition metal oxide heterointerfaces.
