interfaces*

In this talk, I will discuss a model LaAlO₃/SrTiO₃ interface in which conduction t_2g electrons couple to the ferroelectric (FE) phonon mode of the SrTiO₃ substrate. Within a self-consistent phonon theory that captures the quantum critical behavior of the FE transition, we show that proximity to the quantum critical point leads to universal tails in the electron density of the form n(z) ∼ (λ+z)⁻², where λ ∼ T^2−d/z, with d = 3 the dimensionality and z = 1 the dynamical critical exponent. Implications for the interface properties at low electron density are discussed.