Lattice density-functional theory on graphene

TL;DR

This paper develops a lattice density-functional theory for graphene, accurately modeling ground-state properties and spin configurations, including impurity effects, by leveraging an exact Hubbard model solution.

Contribution

It introduces a novel density-functional approach on the graphene lattice using an exact Hubbard model reference, considering extended hoppings and parameterized exchange-correlation potentials.

Findings

Accurately predicts ground-state energy and density of graphene flakes and sheets.

Matches exact diagonalization results for small systems with impurities.

Correctly identifies ground-state spin in large graphene flakes.

Abstract

A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correct ground-state spin is found in the case of large triangular and bowtie flakes out of the scope of exact diagonalization methods.