Spin and electronic correlations in gated graphene quantum rings

We present a theory of graphene quantum rings designed to produce degenerate shells of single particle states close to the Fermi level. We show that populating these shells with carriers using a gate leads to correlated ground states with finite total electronic spin. Using a combination of tight-binding and configuration interaction methods we predict ground state and total spin of the system as a function of the filling of the shell. We show that for smaller quantum rings, the spin polarization of the ground state at half filling depends strongly on the size of the system, but reaches a maximum value after reaching a critical size.Comment: 7 pages, 8 figure

Electronic shells of Dirac fermions in graphene quantum rings in a magnetic field

We present results of tight binding calculations demonstrating existence of degenerate electronic shells of Dirac Fermions in narrow, charge neutral graphene quantum rings. We predict removal of degeneracy with finite magnetic field. We show, using a combination of tight binding and configuration interaction methods, that by filling a graphene ring with additional electrons this carbon based structure with half-filled shell acquires a finite magnetic moment.Comment: 10 pages, 4 figure

Electronic properties of gated triangular graphene quantum dots: Magnetism, correlations, and geometrical effects

We present a theory of electronic properties of gated triangular graphene quantum dots with zigzag edges as a function of size and carrier density. We focus on electronic correlations, spin and geometrical effects using a combination of atomistic tight-binding, Hartree-Fock and configuration interaction methods (TB+HF+CI) including long range Coulomb interactions. The single particle energy spectrum of triangular dots with zigzag edges exhibits a degenerate shell at the Fermi level with a degeneracy N_{edge} proportional to the edge size. We determine the effect of the electron-electron interactions on the ground state, the total spin and the excitation spectrum as a function of a shell filling and the degeneracy of the shell using TB+HF+CI for N_{edge} < 12 and approximate CI method for N_{edge}\geq 12. For a half-filled neutral shell we find spin polarized ground state for structures up to N=500 atoms in agreement with previous {\it ab initio} and mean-field calculations, and in agreement with Lieb's theorem for a Hubbard model on a bipartite lattice. Adding a single electron leads to the complete spin depolarization for N_{edge}\leq 9. For larger structures, the spin depolarization is shown to occur at different filling factors. Away from half-fillings excess electrons(holes) are shown to form Wigner-like spin polarized triangular molecules corresponding to large gaps in the excitation spectrum. The validity of conclusions is assessed by a comparison of results obtained from different levels of approximations. While for the charge neutral system all methods give qualitatively similar results, away from the charge neutrality an inclusion of all Coulomb scattering terms is necessary to produce results presented here.Comment: 13 pages, 13 figure

Excitonic absorption in gate controlled graphene quantum dots

We present a theory of excitonic processes in gate controlled graphene quantum dots. The dependence of the energy gap on shape, size and edge for graphene quantum dots with up to a million atoms is predicted. Using a combination of tight-binding, Hartree-Fock and configuration interaction methods, we show that triangular graphene quantum dots with zigzag edges exhibit optical transitions simultaneously in the THz, visible and UV spectral ranges, determined by strong electron-electron and excitonic interactions. The relationship between optical properties and finite magnetic moment and charge density controlled by an external gate is predicted.Comment: ~4 pages, 4 figure

Magnetism and correlations in fractionally filled degenerate shells of graphene quantum dots

When an electron is confined to a triangular atomic thick layer of graphene [1-5] with zig-zag edges, its energy spectrum collapses to a shell of degenerate states at the Fermi level (Dirac point) [6-9]. The degeneracy is proportional to the edge size and can be made macroscopic. This opens up the possibility to design a strongly correlated electronic system as a function of fractional filling of the zero-energy shell, in analogy to the fractional quantum Hall effect in a quasi-two-dimensional electron gas[10], but without the need for a high magnetic field. In this work we show that electronic correlations, beyond the Hubbard model[6,7] and mean-field density functional theory (DFT) [7,8] play a crucial role in determining the nature of the ground state and the excitation spectrum of triangular graphene quantum dots as a function of dot size and filling fraction of the shell of zero-energy states. The interactions are treated by a combination of DFT, tight-binding, Hartree-Fock and configuration interaction methods (TB-HF-CI) and include all scattering and exchange terms within second nearest neighbors as well as interaction with metallic gate. We show that a half filled charge neutral shell leads to full spin polarization of the island but this magnetic moment is completely destroyed by the addition of a single electron, in analogy to the effect of skyrmions on the quantum Hall ferromagnet [11-14] and spin depolarization in electrostatically defined semiconductor quantum dots[15-18]. The depolarization of the ground state is predicted to result in blocking of current through a graphene quantum dot due to spin blockade (SB) [18].Comment: v2: minor corrections, new forma

Zero-energy states in triangular and trapezoidal graphene structures

We derive analytical solutions for the zero-energy states of degenerate shell obtained as a singular eigenevalue problem found in tight-binding (TB) Hamiltonian of triangular graphene quantum dots with zigzag edges. These analytical solutions are in agreement with previous TB and density functional theory (DFT) results for small graphene triangles and extend to arbitrary size. We also generalize these solutions to trapezoidal structure which allow us to study bowtie graphene devices.Comment: 4 pages, 4 figure

Orbital Magnetization of Quantum Spin Hall Insulator Nanoparticles

Both spin and orbital degrees of freedom contribute to the magnetic moment of isolated atoms. However, when inserted in crystals, atomic orbital moments are quenched because of the lack of rotational symmetry that protects them when isolated. Thus, the dominant contribution to the magnetization of magnetic materials comes from electronic spin. Here we show that nanoislands of quantum spin Hall insulators can host robust orbital edge magnetism whenever their highest occupied Kramers doublet is singly occupied, upgrading the spin edge current into a charge current. The resulting orbital magnetization scales linearly with size, outweighing the spin contribution for islands of a few nm in size. This linear scaling is specific of the Dirac edge states and very different from Schrodinger electrons in quantum rings. Modelling Bi(111) flakes, whose edge states have been recently observed, we show that orbital magnetization is robust with respect to disorder, thermal agitation, shape of the island and crystallographic direction of the edges, reflecting its topological protection.Comment: 7 pages, 5 figures, + Supporting Informatio

Zero-energy states of graphene triangular quantum dots in a magnetic field

We present a tight-binding theory of triangular graphene quantum dots (TGQD) with zigzag edge and broken sublattice symmetry in external magnetic field. The lateral size quantization opens an energy gap and broken sublattice symmetry results in a shell of degenerate states at the Fermi level. We derive a semi-analytical form for zero-energy states in a magnetic field and show that the shell remains degenerate in a magnetic field, in analogy to the 0th Landau level of bulk graphene. The magnetic field closes the energy gap and leads to the crossing of valence and conduction states with the zero-energy states, modulating the degeneracy of the shell. The closing of the gap with increasing magnetic field is present in all graphene quantum dot structures investigated irrespective of shape and edge termination.Comment: 8 pages, 7 figure