interface*

Under a film of lanthanum aluminate (LAO) on strontium titanate (STO) a two dimensional metal appears after a critical thickness, as a response to the electrostatic energy build-up originated by the polar discontinuity at the interface. The character of the transition has not been much explored given the discrete character of the controlling parameter, the film thickness. However, an applied electric field across the film for a thickness close to the transition will drive the transition as well, the character of the transition becoming relevant, not only fundamentally but for possible applications, too. A phenomenological mean-field theory predicts a continuous transition, while a saturating discontinuous one has been assumed in other contexts. We will present a theoretical analysis showing a richer phenomenology than expected so far, with the possibility of either continuous or discontinuous transitions, including a situation in which there is a second discontinuous transition with a jump in carrier concentration after an earlier continuous metal-insulator one.