Temperature-Dependent Band Structure of SrTiO$_3$ Interfaces

TL;DR

This paper presents a theoretical model of the temperature-dependent electronic band structure at SrTiO3 interfaces, revealing significant electron redistribution from 2D interface states to 3D tails as temperature decreases, especially at low electron densities.

Contribution

The study introduces a comprehensive model combining tight-binding and Landau-Devonshire theory to analyze temperature effects on interfacial electron distribution in SrTiO3-based heterostructures.

Findings

Electrons shift from interface to 3D tails as temperature drops.

Low-density electron gases exhibit substantial redistribution.

The model explains high-mobility components observed in experiments.

Abstract

We build a theoretical model for the electronic properties of the two-dimensional (2D) electron gas that forms at the interface between insulating SrTiO$_3$ and a number of polar cap layers, including LaTiO$_3$, LaAlO$_3$, and GdTiO$_3$. The model treats conduction electrons within a tight-binding approximation, and the dielectric polarization via a Landau-Devonshire free energy that incorporates strontium titanate's strongly nonlinear, nonlocal, and temperature-dependent dielectric response. The self-consistent band structure comprises a mix of quantum 2D states that are tightly bound to the interface, and quasi-three-dimensional (3D) states that extend hundreds of unit cells into the SrTiO$_3$ substrate. We find that there is a substantial shift of electrons away from the interface into the 3D tails as temperature is lowered from 300 K to 10 K. This shift is least important at high electron densities ($\sim 10^{14}$ cm$^{-2}$), but becomes substantial at low densities; for example, the total electron density within 4~nm of the interface changes by a factor of two for 2D electron densities $\sim 10^{13}$ cm$^{-2}$. We speculate that the quasi-3D tails form the low-density high-mobility component of the interfacial electron gas that is widely inferred from magnetoresistance measurements.