Influence of the ferroelectric quantum critical point on SrTiO$_3$ interfaces

TL;DR

This paper investigates how proximity to a ferroelectric quantum critical point influences electron behavior at SrTiO3 interfaces, revealing universal density tails and implications for metal-insulator transitions.

Contribution

It introduces a self-consistent phonon model capturing quantum critical behavior and predicts universal electron density tails near the critical point.

Findings

Electron density exhibits universal tails decaying as $( ext{const}+z)^{-2}$.

The tail decay length $ ext{lambda}$ scales with temperature as $T^{2-d/\mathfrak{z}}$.

Implications for the metal-insulator transition at low electron densities are discussed.

Abstract

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.