Hubbard-Thomas-Fermi Theory of Transition Metal Oxide Heterostructures

TL;DR

This paper introduces a Thomas-Fermi approximation for modeling charge distributions in transition metal oxide heterostructures, simplifying complex calculations while maintaining accuracy compared to Hartree-Fock results.

Contribution

The work develops a simplified Thomas-Fermi approach for transition metal oxides that accurately reproduces Hartree-Fock results and offers qualitative insights.

Findings

Thomas-Fermi theory matches Hartree-Fock results for heterostructures

Electrostatic energy can be easily computed with charged sheets approximation

The approach provides qualitative estimates of key properties

Abstract

We demonstrate that the charge distributions in Hubbard-model representations of transition metal oxide heterojucntions can be described by a Thomas-Fermi theory in which the energy is approximated as the sum of the electrostatic energy and the uniform three-dimensional Hubbard model energy per site at the local density equals to a constant. When charged atomic layers in the oxides are approximated as two-dimensional sheets with uniform charge density, the electrostatic energy is simply evaluated. We find that this Thomas-Fermi theory can reproduce results obtained from full Hartree-Fock theory for various different heterostructures. We also show explicitly how Thomas-Fermi theory can be used to estimate some key properties qualitatively.