Lattice density-functional theory on graphene

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.

References in corpus (5)

• Edge-dependent selection rules in magic triangular graphene flakes
• Electronic structure of triangular, hexagonal and round graphene flakes near the Fermi level
• Spintronic Properties of Zigzag-Edged Triangular Graphene Flakes
• Electronic shell and supershell structure in graphene flakes
• Density-functional theory for the Hubbard model: numerical results for the Luttinger liquid and the Mott insulator

Cited by in corpus (14)

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• Site-Occupation Embedding Theory using Bethe Ansatz Local Density Approximations
• Interacting fermions in 1D disordered lattices: Exploring localization and transport properties with lattice density-functional theories
• Time-dependent bond-current functional theory for lattice Hamiltonians: fundamental theorem and application to electron transport
• Ground-state magnetic phase diagram of bow-tie graphene nanoflakes in external magnetic field
• Electric field control of the indirect magnetic coupling through a short graphene nanoribbon
• Density-functional theory approach to the thermodynamics of the harmonically confined one-dimensional Hubbard model
• Geometrical Perspective on Spin-Lattice Density-Functional Theory
• Extensibility of Hohenberg-Kohn Theorem to general quantum systems
• Solving one-body ensemble N-representability problems with spin
• Refining ensemble $N$-representability of one-body density matrices from partial information
• Density-Functional Theory on Graphs