Effective low-energy Hamiltonians for interacting nanostructures

We present a functional renormalization group (fRG) treatment of trigonal graphene nanodiscs and composites thereof, modeled by finite-size Hubbard-like Hamiltonians with honeycomb lattice structure. At half filling, the noninteracting spectrum of these structures contains a certain number of half-filled states at the Fermi level. For the case of trigonal nanodiscs, including interactions between these degenerate states was argued to lead to a large ground state spin with potential spintronics applications. Here we perform a systematic fRG flow where the excited single-particle states are integrated out with a decreasing energy cutoff, yielding a renormalized low-energy Hamiltonian for the zero-energy states that includes effects of the excited levels. The numerical implementation corroborates the results obtained with a simpler Hartree-Fock treatment of the interaction effects within the zero-energy states only. In particular, for trigonal nanodiscs the degeneracy of the one-particle-states with zero-energy turns out to be very robust against influences of the higher levels. As an explanation, we give a general argument that within this fRG scheme the zero-energy degeneracy remains unsplit under quite general conditions and for any size of the trigonal nanodisc. We furthermore discuss the differences in the effective Hamiltonian and their ground states of single nanodiscs and composite bow-tie-shaped systems.Comment: 13 page

Mathematical applications of inductive logic programming

Accepted versio

Few simple rules governing hydrogenation of graphene dots

We investigated binding of hydrogen atoms to small Polycyclic Aromatic Hydrocarbons (PAHs) - i.e. graphene dots with hydrogen-terminated edges - using density functional theory and correlated wavefunction techniques. We considered a number of PAHs with 3 to 7 hexagonal rings and computed binding energies for most of the symmetry unique sites, along with the minimum energy paths for significant cases. The chosen PAHs are small enough to not present radical character at their edges, yet show a clear preference for adsorption at the edge sites which can be attributed to electronic effects. We show how the results, as obtained at different level of theory, can be rationalized in detail with the help of few simple concepts derivable from a tight-binding model of the $\pi$ electrons

Topological Frustration in Graphene Nanoflakes: Magnetic Order and Spin Logic Devices

Magnetic order in graphene-related structures can arise from size effects or from topological frustration. We introduce a rigorous classification scheme for the types of finite graphene structures (nano-flakes) which lead to large net spin or to antiferromagnetic coupling between groups of electron spins. Based on this scheme, we propose specific examples of structures that can serve as the fundamental (NOR and NAND) logic gates for the design of high-density ultra-fast spintronic devices. We demonstrate, using ab initio electronic structure calculations, that these gates can in principle operate at room temperature with very low and correctable error rates.Comment: Typo in title fixe

Emergence of magnetism in graphene materials and nanostructures

Magnetic materials and nanostructures based on carbon offer unique opportunities for future technological applications such as spintronics. This article reviews graphene-derived systems in which magnetic correlations emerge as a result of reduced dimensions, disorder and other possible scenarios. In particular, zero-dimensional graphene nanofragments, one-dimensional graphene nanoribbons, and defect-induced magnetism in graphene and graphite are covered. Possible physical mechanisms of the emergence of magnetism in these systems are illustrated with the help of computational examples based on simple model Hamiltonians. In addition, this review covers spin transport properties, proposed designs of graphene-based spintronic devices, magnetic ordering at finite temperatures as well as the most recent experimental achievements.Comment: tutorial-style review article -- 18 pages, 19 figure