Hyperfine interactions, magnetic interactions between the spins of electrons and nuclei, in graphene and related carbon nanostructures are studied. By using a combination of accurate first principles calculations on graphene fragments and statistical analysis, I show that both isotropic and dipolar hyperfine interactions can be accurately described in terms of the local electron spin distribution and atomic structure. A complete set of parameters describing the hyperfine interactions of 13 C and other nuclear spins at substitution impurities and edge terminations is determined.PACS numbers: 71.70. Jp, 81.05.Uw, 03.67.Pp Graphene and related carbon nanostructures are considered as potential building blocks of future electronics, including spintronics [1] and quantum information processing based on electron spins [2] or nuclear spins [3]. Carbon nanostructures are attractive for these applications because of the weak spin-orbit interaction in materials made of light elements [4,5]. Promising results for the spin-polarized current lifetimes in carbon nanotubes [6,7,8] and graphene [9] unambiguously confirm the potential of these materials. A number of quantum dot devices, components of solid-state quantum computers, based on carbon nanostructures have been proposed recently [10,11,12,13]. Hyperfine interactions (HFIs), the weak magnetic interactions between the spins of electrons and nuclei, become increasingly important on the nanoscale. In carbon nanostructures the interactions of electron spins with an ensemble of nuclear spins are expected to be the leading contribution to the electron spin decoherence [4,7,14]. Minimizing HFIs is thus necessary for achieving longer electron spin coherence times [15]. In some other instances the HFIs play an important role as a link between the spins of electrons and nuclei in the nanostructures [3,16,17,18] underlying the implementations of quantum information processing involving nuclear spins. Probing HFIs with magnetic resonance techniques also provides a wealth of information about structure and dynamics of carbon materials [19]. A common understanding and an ability to control the HFIs are thus necessary for engineering future electronic devices based on graphene and related nanostructures.In this Letter, I study the hyperfine interactions in carbon nanostructures by using a combination of accurate first principles calculations on graphene fragments and statistical analysis. I show that the interaction of the conduction (low-energy) π electron spins with nuclear spins can be described in terms of only the local (on-site and first-nearest-neighbor) π electron spin distribution and the local atomic structure. The conduction electron spin distribution can be determined using simpler computational approaches (e.g. tight binding or analytical approximations [20,21]) and tuned by tailoring nanos-
FIG. 1: (Color online). Projections of the spin-polarized conduction electron density ρ s c (r) (a) and the total spin density ρ s (r) (b) on the plane of an electron-doped graphene...