Transport, Aharonov-Bohm, and Topological Effects in Graphene Molecular Junctions and Graphene Nanorings

The unique ultra-relativistic, massless, nature of electron states in two-dimensional extended graphene sheets, brought about by the honeycomb lattice arrangement of carbon atoms in two-dimensions, provides ingress to explorations of fundamental physical phenomena in graphene nanostructures. Here we explore the emergence of new behavior of electrons in atomically precise segmented graphene nanoribbons (GNRs) and graphene rings with the use of tight-binding calculations, non-equilibrium Green's function transport theory, and a newly developed Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass-barriers at the contacts between segments. Through transport investigations in variable-width segmented GNRs with armchair, zigzag, and mixed edge terminations we uncover development of new Fabry-Perot-like interference patterns in segmented GNRs, a crossover from the ultra-relativistic massless regime, characteristic of extended graphene systems, to a massive relativistic behavior in narrow armchair GNRs, and the emergence of nonrelativistic behavior in zigzag-terminated GNRs. Evaluation of the electronic states in a polygonal graphene nanoring under the influence of an applied magnetic field in the Aharonov-Bohm regime, and their analysis with the use of a relativistic quantum-field theoretical model, unveils development of a topological-in-origin zero-energy soliton state and charge fractionization. These results provide a unifying framework for analysis of electronic states, coherent transport phenomena, and the interpretation of forthcoming experiments in segmented graphene nanoribbons and polygonal rings.Comment: 5 figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/. in J. Phys. Chem. C (2015), article ASAP. arXiv admin note: substantial text overlap with arXiv:1502.0020

Bosonic molecules in rotating traps

We present a variational many-body wave function for repelling bosons in rotating traps, focusing on rotational frequencies that do not lead to restriction to the lowest Landau level. This wave function incorporates correlations beyond the Gross-Pitaevskii (GP) mean field approximation, and it describes rotating boson molecules (RBMs) made of localized bosons that form polygonal-ring-like crystalline patterns in their intrinsic frame of reference. The RBMs exhibit characteristic periodic dependencies of the ground-state angular momenta on the number of bosons in the polygonal rings. For small numbers of neutral bosons, the RBM ground-state energies are found to be always lower than those of the corresponding GP solutions, in particular in the regime of GP vortex formation.Comment: To appear in Phys. Rev. Lett. LATEX, 5 pages with 5 figures. For related papers, see http://www.prism.gatech.edu/~ph274cy

Edge and bulk components of lowest-Landau-level orbitals, correlated fractional quantum Hall effect incompressible states, and insulating behavior in finite graphene samples

Many-body calculations of the total energy of interacting Dirac electrons in finite graphene samples exhibit joint occurrence of cusps at angular momenta corresponding to fractional fillings characteristic of formation of incompressible (gapped) correlated states (nu=1/3 in particular) and opening of an insulating energy gap (that increases with the magnetic field) at the Dirac point, in correspondence with experiments. Single-particle basis functions obeying the zigzag boundary condition at the sample edge are employed in exact diagonalization of the interelectron Coulomb interaction, showing, at all sizes, mixed equal-weight bulk and edge components. The consequent depletion of the bulk electron density attenuates the fractional-quantum-Hall-effect excitation energies and the edge charge accumulation results in a gap in the many-body spectrum.Comment: 8 pages with 7 figures. REVTEX4. For related publications, see http://www.prism.gatech.edu/~ph274c

Crystalline boson phases in harmonic traps: Beyond the Gross-Pitaevskii mean field

Strongly repelling bosons in two-dimensional harmonic traps are described through breaking of rotational symmetry at the Hartree-Fock level and subsequent symmetry restoration via projection techniques, thus incorporating correlations beyond the Gross-Pitaevskii (GP) solution. The bosons localize and form polygonal-ring-like crystalline patterns, both for a repulsive contact potential and a Coulomb interaction, as revealed via conditional-probability-distribution analysis. For neutral bosons, the total energy of the crystalline phase saturates in contrast to the GP solution, and its spatial extent becomes smaller than that of the GP condensate. For charged bosons, the total energy and dimensions approach the values of classical point-like charges in their equilibrium configuration.Comment: Published version. Typos corrected. REVTEX4; 5 pages with 3 PS figures. For related papers, see http://www.prism.gatech.edu/~ph274c

Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field

We investigate the way that the degenerate manifold of midgap edge states in quasicircular graphene quantum dots with zig-zag boundaries supports, under free-magnetic-field conditions, strongly correlated many-body behavior analogous to the fractional quantum Hall effect (FQHE), familiar from the case of semiconductor heterostructures in high magnetic fields. Systematic exact-diagonalization (EXD) numerical studies are presented for the first time for 5 <= N <= 8 fully spin-polarized electrons and for total angular momenta in the range of N(N-1)/2 <= L <= 150. We present a derivation of a rotating-electron-molecule (REM) type wave function based on the methodology introduced earlier [C. Yannouleas and U. Landman, Phys. Rev. B 66, 115315 (2002)] in the context of the FQHE in two-dimensional semiconductor quantum dots. The EXD wave functions are compared with FQHE trial functions of the Laughlin and the derived REM types. It is found that a variational extension of the REM offers a better description for all fractional fillings compared with that of the Laughlin functions (including total energies and overlaps), a fact that reflects the strong azimuthal localization of the edge electrons. In contrast with the multiring arrangements of electrons in circular semiconductor quantum dots, the graphene REMs exhibit in all instances a single (0,N) polygonal-ring molecular (crystalline) structure, with all the electrons localized on the edge. Disruptions in the zig-zag boundary condition along the circular edge act effectively as impurities that pin the electron molecule, yielding single-particle densities with broken rotational symmetry that portray directly the azimuthal localization of the edge electrons.Comment: Revtex. 14 pages with 13 figures and 2 tables. Physical Review B, in press. For related papers, see http://www.prism.gatech.edu/~ph274cy

Patterns of the Aharonov-Bohm oscillations in graphene nanorings

Using extensive tight-binding calculations, we investigate (including the spin) the Aharonov-Bohm (AB) effect in monolayer and bilayer trigonal and hexagonal graphene rings with zigzag boundary conditions. Unlike the previous literature, we demonstrate the universality of integer (hc/e) and half-integer (hc/2e) values for the period of the AB oscillations as a function of the magnetic flux, in consonance with the case of mesoscopic metal rings. Odd-even (in the number of Dirac electrons, N) sawtooth-type patterns relating to the halving of the period have also been found; they are more numerous for a monolayer hexagonal ring, compared to the cases of a trigonal and a bilayer hexagonal ring. Additional more complicated patterns are also present, depending on the shape of the graphene ring. Overall, the AB patterns repeat themselves as a function of N with periods proportional to the number of the sides of the rings.Comment: REVTEX 4-1, 6 pages with 7 figures. For related papers, see http://www.prism.gatech.edu/~ph274cy