Influence of the ferroelectric quantum critical point on SrTiO$_3$   interfaces
  We study a model SrTiO$_3$ interface in which conduction $t_{2g}$ electrons couple to the ferroelectric (FE) phonon mode. We treat the FE mode within a self-consistent phonon theory that captures its quantum critical behavior, and show that proximity to the quantum critical point leads to universal tails in the electron density of the form $n(z) \sim (\lambda+z)^{-2}$, where $\lambda \sim T^{2-d/\mathfrak{z}}$, with $d=3$ the dimensionality and $\mathfrak{z}=1$ the dynamical critical exponent. Implications for the metal-insulator transition at low electron density are discussed. 
W. A. Atkinson, P. Lafleur, and A. Raslan
cond-mat.str-el cond-mat.mtrl-sci