Dirac reduction for nonholonomic mechanical systems and semidirect products

This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange–Dirac and Hamilton–Dirac dynamical systems. This reduction procedure is accompanied by reduction of the associated variational structures on both Lagrangian and Hamiltonian sides. The reduced dynamical systems obtained are called the implicit Euler–Poincaré–Suslov equations with advected parameters and the implicit Lie–Poisson–Suslov equations with advected parameters. The theory is illustrated with the help of finite and infinite dimensional examples. It is shown that equations of motion for second order Rivlin–Ericksen fluids can be formulated as an infinite dimensional nonholonomic system in the framework of the present paper.     

Small Data Scattering for the One-Dimensional Nonlinear Dirac Equation with Power Nonlinearity

We study scattering problems for the one-dimensional nonlinear Dirac equation (?_t + α?_x + iβ)Φ = λ|Φ|^p?1Φ. We prove that if p > 3 (resp. p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space. In order to prove these results, we use linear operators D(t)xD(?t) and t?_x + x?_t ? α/2, where {D(t)}_t∈? is the free Dirac evolution group. For the reader's convenience, in an appendix we list and prove fundamental properties of D(t)xD(?t) and t?_x + x?_t ? α/2.     

Density functional study of α-graphyne derivatives: Energetic stability,atomic and electronic structure

The energetic stability, atomic and electronic structures of α-graphyne and its derivatives (α-GYs) with extended carbon chains were investigated by density functional (DF) calculations in this work. The studied α-GYs consist of hexagon carbon rings sharing their edges with carbon atoms N=1–10. The structure and energy analyses show that α-GYs with even-numbered carbon chains have alternating single and triple C–C bonds (polyyne), energetically more stable than those with odd-numbered carbon chains possessing continuous double C–C bonds (polycumulene). The calculated electronic structures indicate that α-GYs can be either metallic (odd N) or semiconductive (even N) depending on the parity of number of atoms on hexagon edges despite the edge length. The semiconducting α-graphyne derivatives are found to possess Dirac cones (DC) with small direct band gaps 2–40 meV and large electron velocities 0.554×10⁶–0.671×10⁶ m/s, 70–80% of that of graphene. Our DF studies suggest that introducing sp carbon atoms into the hexagon edges of graphene opens up an avenue to switch between metallic and DC electronic structures via tuning the parity of the number of hexagon edge atoms.     

The effect of two ferromagnetic metal stripes on valley polarization of electrons in a graphene

As the key factor for designing the valleytronic devices is to well understand the valley-dependent transport mechanism in graphene, we investigate, in this work, the effect of two ferromagnetic (FM) metal stripes on the valley polarization in a graphene nanostructure with a strain. The nearly 100% valley polarization is observed at certain energy windows and it can be easily controlled through changing the width and the position of the FM stripe as well as the strength of the magnetic field induced by the FM stripe. Our interesting findings reveal the valley-dependent transport mechanism of electrons and promote the realization of the new types of valleytronic devices modulated by the FM stripe and the strain.     

Extended Dirac oscillator in (2 + 1)-dimensional space-time

We consider a soluble covariant extension of the two-dimensional Dirac oscillator (2D DO), which breaks the infinite degeneracy of the energy spectrum. The energy eigenvalues and the corresponding eigenstates of the system are obtained algebraically using chiral creation and annihilation operators. The effect of the coupling to an external constant transverse magnetic field is investigated. The connection with Jaynes-Cummings (JC) and Anti-Jaynes-Cummings (AJC) models of quantum optics, and other features of the system are also discussed.     

Novel conductance step in carbon nanotube with wing-like zigzag graphene nanoribbons

Connecting one armchair carbon nanotube(CNT) to several zigzag graphene nanoribbons(ZGNRs) we find that the topologically-protected edge states of ZGNRs and the massless Dirac particle inherited from CNT still hold from the analysis of the band structure and the edge state. Furthermore, the lowest conductance step at the valley bottom increases proportionally with increasing the number of ZGNR wings. A novel conductance step of a peak occurs in the valley, which is two steps higher than the lowest step at the valley bottom. In addition, with increasing the number of ZGNR wings the width of the novel conductance step becomes narrow.     

Stability of equilibrium solutions of a double power reaction-diffusion equation with a Dirac interaction

In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction-diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed.     

Gap opening and tuning in single-layer graphene with combined electric and magnetic field modulation

The energy band structure of single-layer graphene under one-dimensional electric and magnetic field modulation is theoretically investigated. The criterion for bandgap opening at the Dirac point is analytically derived with a two-fold degeneracy second-order perturbation method. It is shown that a direct or an indirect bandgap semiconductor could be realized in a single-layer graphene under some specific configurations of the electric and magnetic field arrangement. Due to the bandgap generated in the single-layer graphene,the Klein tunneling observed in pristine graphene is completely suppressed.