Igor Romanovsky

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

Strongly-interacting 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-ringlike 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 pointlike charges in their equilibrium configuration.

Topological effects and particle-physics analogies beyond the massless Dirac-Weyl fermion in graphene nanorings

Armchair and zigzag edge terminations in planar hexagonal and trigonal graphene nanorings are shown to underlie one-dimensional topological states associated with distinctive energy gaps and patterns (e.g., linear dispersion of the energy of an hexagonal ring with an armchair termination versus parabolic dispersion for a zigzag terminated one) in the bands of the tight-binding spectra as a function of the magnetic field. A relativistic Dirac-Kronig-Penney model analysis of the tight-binding Aharonov-Bohm behavior reveals that the graphene quasiparticle in an armchair hexagonal ring is a condensed-matter realization of an ultrarelativistic fermion with a position-dependent mass term, akin to the zero-energy fermionic solitons with fractional charge familiar from quantum-field theory and from the theory of polyacetylene. The topological origins of the above behavior are highlighted by contrasting it with the case of a trigonal armchair ring, where we find that the quasiparticle excitations behave as familiar Dirac fermions with a constant mass. Furthermore, the spectra of a zigzag hexagonal ring correspond to the low-kinetic-energy nonrelativistic regime of a lepton-like massive fermion. A one-dimensional relativistic Lagrangian formalism coupling a fermionic and a scalar bosonic field via a Yukawa interaction, in conjunction with the breaking of the

Patterns of the Aharonov-Bohm oscillations in graphene nanorings

{Z}_{2}

Beyond the constant-mass Dirac physics: Solitons, charge fractionization, and the emergence of topological insulators in graphene rings

reflectional symmetry of the scalar field, is shown to unify the above dissimilar behaviors.

Thermoelectric effects in a Luttinger liquid

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.

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

The doubly-connected polygonal geometry of planar graphene rings is found to bring forth topological configurations for accessing nontrivial relativistic quantum field (RQF) theory models that carry beyond the constant-mass Dirac-fermion theory. These include generation of sign-alternating masses, solitonic excitations, and charge fractionization. The work integrates a RQF Lagrangian formulation with numerical tight-binding Aharonov-Bohm electronic spectra and the generalized position-dependent-mass Dirac equation. In contrast to armchair graphene rings (aGRGs) with pure metallic arms, certain classes of aGRGs with semiconducting arms, as well as with mixed metallic-semiconducting ones, are shown to exhibit properties of one-dimensional nontrivial topological insulators. This further reveals an alternative direction for realizing a graphene-based nontrivial topological insulator through the manipulation of the honeycomb lattice geometry, without a spin-orbit contribution.

Aharonov-Bohm effect and plasma oscillations in superconducting tubes and rings

Thermoelectric effects in a Luttinger liquid (LL) wire adiabatically connected to the leads of noninteracting electrons are considered. For a multichannel LL a staircase-like behavior of the thermal conductance as a function of chemical potential is found. The thermopower for a LL wire with an impurity is evaluated for two cases: (i) LL constriction, and (ii) infinite LL wire. We show that the thermopower is described a Mott-like formula renormalized by an interaction-dependent factor. For an infinite LL the renormalization factor decreases with increase of the interaction. However, for a realistic situation, when a LL wire is connected to the leads of noninteracting electrons (LL constriction), the repulsive electron-electron interaction enhances the thermopower. A nonlinear Peltier effect in a LL is briefly discussed.

Phase-controlled force and magnetization oscillations in superconducting ballistic nanowires.

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.

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

Low frequency plasma oscillations in superconducting tubes are considered. The emergence of two different dimensionality regimes of plasma oscillations in tubes, exhibiting a crossover from one-dimensional to two-dimensional behavior, depending on whether

Unique nature of the lowest Landau level in finite graphene samples with zigzag edges: Dirac electrons with mixed bulk-edge character

k R\ll 1