Dual critical thickness for lattice and electronic instabilities in the LaAlO$_{3}$/SrTiO$_{3}$ interface.

When matter is strongly downscaled, entirely new properties can emerge that are not present in the parent bulk crystals. A paradigmatic example is the quantum well formed at the interface between SrTiO$_{3}$ (STO) and LaAlO$_{3}$ (LAO). Their charge mismatch leads to a built-in electric field inside the LAO film, which eventually induces the formation of a two-dimensional electron system at the boundary. In addition to this electronic reconstruction, here we show that the LAO/STO system also undergoes a ``phononic reconstruction'' strongly coupled to the inbuilt electric fields. More specifically, we have discovered an unexpected mechanism whereby nonpolar antiferrodistortive rotations of AlO$_{6}$ octahedra couple to the internal electrostatic fields. Two basic facts can explain such an unanticipated observation: (i) the extreme confinement of LAO vibration modes, which leads to a ``phonon reconstruction'' that has been so far overlooked; (ii) the emergence and subsequent decline of internal electric fields, resulting from the polar/nonpolar character of this interface. Such internal fields modulate the intensity of the antiferrodistortive modes, providing a new pathway to tailor functional properties that can be extrapolated to other oxide interfaces, beyond the case studied here.