Macroscopic description of the two-dimensional LaAlO$_3$/SrTiO$_3$ interface

TL;DR

This paper introduces a macroscopic analytical model using drift-diffusion equations to explain the emergence of metallic conductivity at the LaAlO3/SrTiO3 interface, aligning well with experimental observations.

Contribution

It presents a simple, macroscopic approach to model the 2D interface conductivity, highlighting the conditions for metallic behavior based on material properties.

Findings

Same type of conductivity in both materials leads to 2D metallic interface

Opposite types of conductivity result in 3D metallic transition

Model results agree with experimental data

Abstract

We propose a simple analytical model to explain possible appearance of the metallic conductivity in the two-dimensional (2D) LaAlO$_3$/SrTiO$_3$ interface. Our model considers the interface within a macroscopic approach which is usual to semiconductor heterojunctions and is based on drift-diffusion equations. The solution of these equations allows to obtain the positions of band edges as a function of distances from the interface. We show that for the 2D metallic conductivity to appear at the interface, the constituting substances should have the same type (either electronic or hole) of conductivity; in the opposite case the possible transition to metallic phase has a three-dimensional character. The results of our model calculations are in agreement with available experimental data.