Hubbard-Thomas-Fermi Theory of Transition Metal Oxide Heterostructures

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.