Wigner crystallization at graphene edges

Using many-body configuration interaction techniques we show that Wigner crystallization occurs at the zigzag edges of graphene at surprisingly high electronic densities up to $0.8$ \mbox{nm}^{-1}. In contrast with one-dimensional electron gas, the flat-band structure of the edge states makes the system interaction dominated, facilitating the electronic localization. The resulting Wigner crystal manifests itself in pair-correlation functions, and evolves smoothly as the edge electron density is lowered. We also show that the crystallization affects the magnetization of the edges. While the edges are fully polarized when the system is charge neutral (i.e. high density), above the critical density, the spin-spin correlations between neighboring electrons go through a smooth transition from antiferromagnetic to magnetic coupling as the electronic density is lowered.Comment: 4.5 pages, 4 figure

Defect induced Anderson localization and magnetization in graphene quantum dots

We theoretically investigate the effects of atomic defect related short-range disorders and electron-electron interactions on Anderson type localization and the magnetic properties of hexagonal armchair graphene quantum dots using an extended mean-field Hubbard model. We observe that randomly distributed defects with concentrations between 1-5\% of the total number of atoms leads to localization alongside magnetic puddle-like structures. We show that localization lenght is not affected by magnetization if there is an even distribution of defects between the two sublattices of the honeycomb lattice. However, for an uneven distributions, localization is found to be significantly enhanced

Effects of interedge scattering on the Wigner crystallization in graphene nanoribbons

We investigate the effects of coupling between the two zigzag edges of graphene nanoribbons on the Wigner crystallization of electrons and holes using a combination of tight-binding, mean field Hubbard and many-body configuration interaction methods. We show that the thickness of the nanoribbon plays a crucial role in the formation of Wigner crystal. For ribbon widths smaller than 16 \mbox{\AA}, increased kinetic energy overcomes the long-range Coulomb repulsion and suppresses the Wigner crystallization. For wider ribbons up to 38 \mbox{\AA} wide, strong Wigner localization is observed for even number of electrons, revealing an even-odd effect also found in Coulomb blockade addition spectrum. Interedge correlations are found to be strong enough to allow simultaneous crystallization on both edges, although an applied electric field can decouple the two edges. Finally, we show that Wigner crystallization can also occurs for holes, albeit weaker than for electrons.Comment: Accepted for publication in PR

Effects of long-range disorder and electronic interactions on the optical properties of graphene quantum dots

We theoretically investigate the effects of long-range disorder and electron-electron interactions on the optical properties of hexagonal armchair graphene quantum dots consisting of up to 10806 atoms. The numerical calculations are performed using a combination of tight-binding, mean-field Hubbard and configuration interaction methods. Imperfections in the graphene quantum dots are modelled as a long-range random potential landscape, giving rise to electron-hole puddles. We show that, when the electron-hole puddles are present, tight-binding method gives a poor description of the low-energy absorption spectra compared to meanfield and configuration interaction calculation results. As the size of the graphene quantum dot is increased, the universal optical conductivity limit can be observed in the absorption spectrum. When disorder is present, calculated absorption spectrum approaches the experimental results for isolated monolayer of graphene sheet

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

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

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

The maximum density droplet to lower density droplet transition in quantum dots

We show that, Landau level mixing in two-dimensional quantum dot wave functions can be taken into account very effectively by multiplying the exact lowest Landau level wave functions by a Jastrow factor which is optimized by variance minimization. The comparison between exact diagonalization and fixed phase diffusion Monte Carlo results suggests that the phase of the many-body wave functions are not affected much by Landau level mixing. We apply these wave functions to study the transition from the maximum density droplet state (incipient integer quantum Hall state with angular momentum L=N(N-1)/2) to lower density droplet states (L>N(N-1)/2).Comment: 8 pages, 5 figures, accepted for publication in Phys. Rev.

Interaction-Induced Strong Localization in Quantum Dots

We argue that Coulomb blockade phenomena are a useful probe of the cross-over to strong correlation in quantum dots. Through calculations at low density using variational and diffusion quantum Monte Carlo (up to r_s ~ 55), we find that the addition energy shows a clear progression from features associated with shell structure to those caused by commensurability of a Wigner crystal. This cross-over (which occurs near r_s ~ 20 for spin-polarized electrons) is, then, a signature of interaction-driven localization. As the addition energy is directly measurable in Coulomb blockade conductance experiments, this provides a direct probe of localization in the low density electron gas.Comment: 4 pages, published version, revised discussio