Scaled tight binding model for a two dimensional electron gas at the (001) LaAlO$_3$/SrTiO$_3$ interface

TL;DR

This paper introduces a scaled tight-binding model for simulating the two-dimensional electron gas at the LAO/STO interface, significantly reducing computational time while maintaining accuracy for nanostructure simulations.

Contribution

A novel scaled tight-binding approach that enables efficient and accurate quantum transport and electronic structure simulations of LAO/STO nanostructures.

Findings

Scaled model closely matches the ordinary model up to a factor of 8.

Enables larger mesh sizes, reducing computational cost.

Facilitates realistic size simulations for experimental nanostructures.

Abstract

The progress in the fabrication of nanoscale systems based on the two-dimensional electron gas at the interface between LaAlO$_3$ and SrTiO$_3$ (LAO/STO) has created an increased demand for simulations of these nanostructures, which typically range in size from tens to hundreds of nanometers. Due to the low lattice constant of LAO/STO, approximately 0.394 nm, these calculations become extremely time-consuming. Here, we present a scaled tight-binding approximation defined on a mesh with size that can be several times larger than in the ordinary approach. The scaled model is analyzed within the context of quantum transport simulations and electronic structure calculations. Our findings demonstrate that the scaled model closely aligns with the ordinary one up to a scaling factor of 8. These results pave the way for more efficient simulations of LAO/STO nanostructures with realistic sizes relevant to experimental applications.