Theory of Hyperfine Interactions in Graphene-Based Nanostructures: σ - π Correlations

Open-shell nanographene molecules offer unique possibilities in applications such as spintronics and quantum computing due to their novel physical properties related to magnetism and unconventional topological phases of matter. We focus on the electron-nuclear interactions characterized by the hyperfine couplings in these molecular magnets. Using theoretical tools based on all-electron density functional theory (DFT), tight-binding (TB) models with single π-orbitals within the Mean-Field Hubbard (MFH) description, and perturbative techniques, we demonstrate that the physical origin of these hyperfine splittings relates to exchange interactions between π and σ orbitals. Our results establish the well-known McConnell's equation for the proton hyperfine splittings and provide an intuitive way of understanding the electronic structure of the molecule.