Abstract

We present the analytical solution of the mean-field Hubbard model of undoped and doped graphene rectangulenes. These are non-chiral graphene rectangles of arbitrary length and width, and nanoribbons are thus narrow rectangulenes. We rewrite the Hubbard model in the basis of exact bulk and edge non-interacting eigen-states, and provide analytical expressions for the Coulomb integrals. We also present a general mean-field decoupling of the Hamiltonian, that is valid at any temperature and doping. We introduce the edge-only doping regime and discuss the paramagnetic, ferromagnetic and antiferromagnetic mean-field solutions in this regime. We calculate explicitly at zero temperature the eigen-energies, occupations, spin densities and addition energies of rectangulenes with lengths and widths ranging from a nanometer to several hundreds of them. We rewrite the exact mean-field tight-binding Hamiltonian back in the site-occupation basis.

Abstract

We present the analytical solution of the mean-field Hubbard model of undoped and doped graphene rectangulenes. These are non-chiral graphene rectangles of arbitrary length and width, and nanoribbons are thus narrow rectangulenes. We rewrite the Hubbard model in the basis of exact bulk and edge non-interacting eigen-states, and provide analytical expressions for the Coulomb integrals. We also present a general mean-field decoupling of the Hamiltonian, that is valid at any temperature and doping. We introduce the edge-only doping regime and discuss the paramagnetic, ferromagnetic and antiferromagnetic mean-field solutions in this regime. We calculate explicitly at zero temperature the eigen-energies, occupations, spin densities and addition energies of rectangulenes with lengths and widths ranging from a nanometer to several hundreds of them. We rewrite the exact mean-field tight-binding Hamiltonian back in the site-occupation basis.

Abstract

We present the analytical solution of the mean-field Hubbard model of undoped and doped graphene rectangulenes. These are non-chiral graphene rectangles of arbitrary length and width, and nanoribbons are thus narrow rectangulenes. We rewrite the Hubbard model in the basis of exact bulk and edge non-interacting eigen-states, and provide analytical expressions for the Coulomb integrals. We also present a general mean-field decoupling of the Hamiltonian, that is valid at any temperature and doping. We introduce the edge-only doping regime and discuss the paramagnetic, ferromagnetic and antiferromagnetic mean-field solutions in this regime. We calculate explicitly at zero temperature the eigen-energies, occupations, spin densities and addition energies of rectangulenes with lengths and widths ranging from a nanometer to several hundreds of them. We rewrite the exact mean-field tight-binding Hamiltonian back in the site-occupation basis.

Abstract

We present the analytical solution of the mean-field Hubbard model of undoped and doped graphene rectangulenes. These are non-chiral graphene rectangles of arbitrary length and width, and nanoribbons are thus narrow rectangulenes. We rewrite the Hubbard model in the basis of exact bulk and edge non-interacting eigen-states, and provide analytical expressions for the Coulomb integrals. We also present a general mean-field decoupling of the Hamiltonian, that is valid at any temperature and doping. We introduce the edge-only doping regime and discuss the paramagnetic, ferromagnetic and antiferromagnetic mean-field solutions in this regime. We calculate explicitly at zero temperature the eigen-energies, occupations, spin densities and addition energies of rectangulenes with lengths and widths ranging from a nanometer to several hundreds of them. We rewrite the exact mean-field tight-binding Hamiltonian back in the site-occupation basis.