Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice

The core of the vortex in the Neel order parameter for an easy-plane antiferromagnet on honeycomb lattice is demonstrated to bind two zero-energy states. Remarkably, a single electron occupying this mid-gap band has its spin fragmented between the two sublattices: Whereas it yields a vanishing total magnetization it shows a finite Neel order, orthogonal to the one of the assumed background. The requisite easy-plane anisotropy may be introduced by a magnetic field parallel to the graphene layer, for example. The results are relevant for spin-1/2 fermions on graphene's or optical honeycomb lattice, in the strongly interacting regime.Comment: 4 pages; cosmetic changes; published versio

Wigner Oscillators, Twisted Hopf Algebras and Second Quantization

By correctly identifying the role of central extension in the centrally extended Heisenberg algebra h, we show that it is indeed possible to construct a Hopf algebraic structure on the corresponding enveloping algebra U(h) and eventually deform it through Drinfeld twist. This Hopf algebraic structure and its deformed version U^F(h) are shown to be induced from a more fundamental Hopf algebra obtained from the Schroedinger field/oscillator algebra and its deformed version, provided that the fields/oscillators are regarded as odd-elements of the super-algebra osp(1|2n). We also discuss the possible implications in the context of quantum statistics.Comment: 23 page

Bilayer graphene: gap tunability and edge properties

Bilayer graphene -- two coupled single graphene layers stacked as in graphite -- provides the only known semiconductor with a gap that can be tuned externally through electric field effect. Here we use a tight binding approach to study how the gap changes with the applied electric field. Within a parallel plate capacitor model and taking into account screening of the external field, we describe real back gated and/or chemically doped bilayer devices. We show that a gap between zero and midinfrared energies can be induced and externally tuned in these devices, making bilayer graphene very appealing from the point of view of applications. However, applications to nanotechnology require careful treatment of the effect of sample boundaries. This being particularly true in graphene, where the presence of edge states at zero energy -- the Fermi level of the undoped system -- has been extensively reported. Here we show that also bilayer graphene supports surface states localized at zigzag edges. The presence of two layers, however, allows for a new type of edge state which shows an enhanced penetration into the bulk and gives rise to band crossing phenomenon inside the gap of the biased bilayer system.Comment: 8 pages, 3 fugures, Proceedings of the International Conference on Theoretical Physics: Dubna-Nano200

Cyclic and ruled Lagrangian surfaces in complex Euclidean space

We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a Legendrian curve of the 3-sphere or a Legendrian curve of the anti de Sitter 3-space. We also describe ruled Lagrangian surfaces. Finally we characterize those cyclic and ruled Lagrangian surfaces which are solutions to the self-similar equation of the Mean Curvature Flow. Finally, we give a partial result in the case of Hamiltonian stationary cyclic surfaces

Localized states at zigzag edges of bilayer graphene

We report the existence of zero energy surface states localized at zigzag edges of bilayer graphene. Working within the tight-binding approximation we derive the analytic solution for the wavefunctions of these peculiar surface states. It is shown that zero energy edge states in bilayer graphene can be divided into two families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene; (ii) states with finite amplitude over the two layers, with an enhanced penetration into the bulk. The bulk and surface (edge) electronic structure of bilayer graphene nanoribbons is also studied, both in the absence and in the presence of a bias voltage between planes.Comment: 4 pages, 5 figure

Coulomb Interactions and Ferromagnetism in Pure and Doped Graphene

We study the presence of ferromagnetism in the phase diagram of the two-dimensional honeycomb lattice close to half-filling (graphene) as a function of the strength of the Coulomb interaction and doping. We show that exchange interactions between Dirac fermions can stabilize a ferromagnetic phase at low doping when the coupling is sufficiently large. In clean systems, the zero temperature phase diagram shows both first order and second order transition lines and two distinct ferromagnetic phases: one phase with only one type of carriers (either electrons or holes) and another with two types of carriers (electrons and holes). Using the coherent phase approximation (CPA) we argue that disorder further stabilizes the ferromagnetic phase.Comment: 10 pages; published versio