On Dirac Zero Modes in Hyperdiamond Model

Using the SU(5) symmetry of the 4D hyperdiamond and results on the study of 4D graphene given in "Four Dimensional Graphene" (L.B Drissi, E.H Saidi, M. Bousmina, CPM-11-01, Phys. Rev. D (2011)), we engineer a class of 4D lattice QCD fermions whose Dirac operators have two zero modes. We show that generally the zero modes of the Dirac operator in hyperdiamond fermions are captured by a tensor {\Omega}_{{\mu}}^{l} with 4\times5 complex components linking the Euclidean SO(4) vector {\mu}; and the 5-dimensional representation of SU(5). The Bori\c{c}i-Creutz (BC) and the Karsten-Wilzeck (KW) models as well as their Dirac zero modes are rederived as particular realizations of {\Omega}_{{\mu}}^{l}. Other features are also given. Keywords: Lattice QCD, Bori\c{c}i-Creutz and Karsten-Wilzeck models, 4D hyperdiamond, 4D graphene, SU(5) Symmetry.Comment: LaTex, 28 pages, To appear in Phys Rev

Four Dimensional Graphene

Mimicking pristine 2D graphene, we revisit the BBTW model for 4D lattice QCD given in ref.[5] by using the hidden SU(5) symmetry of the 4D hyperdiamond lattice H_4. We first study the link between the H_4 and SU(5); then we refine the BBTW 4D lattice action by using the weight vectors \lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5 of the 5-dimensional representation of SU(5) satisfying {\Sigma}_i\lambda_i=0. After that we study explicitly the solutions of the zeros of the Dirac operator D in terms of the SU(5) simple roots \alpha_1, \alpha_2, \alpha_3, \alpha_4 generating H_4; and its fundamental weights \omega_1, \omega_2, \omega_3, \omega_4 which generate the reciprocal lattice H_4^\ast. It is shown, amongst others, that these zeros live at the sites of H_4^\ast; and the continuous limit D is given by ((id\surd5)/2) \gamma^\muk_\mu with d, \gamma^\mu and k_\mu standing respectively for the lattice parameter of H_4, the usual 4 Dirac matrices and the 4D wave vector. Other features such as differences with BBTW model as well as the link between the Dirac operator following from our construction and the one suggested by Creutz using quaternions, are also given. Keywords: Graphene, Lattice QCD, 4D hyperdiamond, BBTW model, SU(5) Symmetry.Comment: LaTex, 26 pages, 1 figure, To appear in Phys Rev

Halogenation of SiC for band-gap engineering and excitonic functionalization

The optical excitation spectra and excitonic resonances are investigated in systematically functionalized SiC with Fluorine and/or Chlorine utilizing density functional theory in combination with many-body perturbation theory. The latter is required for a realistic description of the energy band-gaps as well as for the theoretical realization of excitons. Structural, electronic and optical properties are scrutinized and show the high stability of the predicted two-dimensional materials. Their realization in laboratory is thus possible. Huge band-gaps of the order of 4 eV are found in the so-called GW approximation, with the occurrence of bright excitons, optically active in the four investigated materials. Their binding energies vary from 0.9 eV to 1.75 eV depending on the decoration choice and in one case, a dark exciton is foreseen to exist in the fully chlorinated SiC. The wide variety of opto-electronic properties suggest halogenated SiC as interesting materials with potential not only for solar cell applications, anti-reflection coatings or high-reflective systems but also for a possible realization of excitonic Bose-Einstein condensation