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We derive a low-energy effective $\mathbf{k}\cdot\mathbf{p}$ Hamiltonians for monolayer C$_{3}$N at the $ \Gamma $ and $ M $ points of the Brillouin zone where the band edge in the conduction and valence band can be found. Our analysis of the electronic band symmetries helps to better understand several results of recent ab-initio calculations[1,2] for the optical properties of this material. We also calculate the Landau level spectrum. We find that the Landau level spectrum in the degenerate conduction bands at the $ \Gamma $ point acquires properties that are reminiscent of the corresponding results in bilayer graphene, but there are important differences as well. Moreover, because of the heavy effective mass, $n$-doped samples may host interesting electron-electron interaction effects., Comment: 10 pages, 5 figures

We investigate theoretically indirect exchange interaction between magnetic impurities mediated by one-dimensional gapped helical states. Such states, containing massive Dirac fermions, may be realized on the edge of a two-dimensional topological insulator when time-reversal symmetry is weakly broken. We find that the indirect exchange interaction consists of Heisenberg, Dzyaloshinsky-Moriya, in-plane and out-of-plane Ising terms. These terms decay exponentially when Fermi level lies inside the bandgap whereas the Dzyaloshinsky-Moriya term has smallest amplitude. Outside the energy gap the massive helical states modify oscillatory behaviors of the range functions so that their periods decrease near the edge of band in terms of energy gap or Fermi energy. In addition, the out-of-plane Ising term vanishes in the case of zero-gap structure but its oscillation amplitude increases versus energy gap and decreases as a function of Fermi energy whereas the oscillation amplitudes of other components remain constant. Analytical results are also obtained for subgap and over gap regimes. Furthermore, the effects of electron-electron interactions are analyzed., Comment: 8 pages, 4 figures

In this study, the effect of alumina and modified alumina nanoparticles in a PMMA/alumina nanocomposite was investigated. To attain this goal, the glass transition behavior of poly methyl methacrylate (PMMA), PMMA/alumina and PMMA/hydroxylated alumina nanocomposites were investigated by molecular dynamic simulations (MD). All the MD simulations were performed using the Materials Studio 6.0 software package of Accelrys. To obtain the glass transition temperature, the variation of density vs. temperature was obtained. The temperature at which the slope of the density-temperature curve observably changes is defined as the glass transition temperature (Tg). The effect of alumina nanoparticles on the Tg was related to the free volume and the mobility of chain segments and the interaction between the alumina nanoparticles and the polymer. The mobility of the chain segments was investigated based on the mean square displacement and radius gyration. The results show that the increasement the Tg of the PMMA/hydroxylated alumina nanocomposite is more than that of the PMMA/alumina nanocomposite due to the modification of the alumina nanoparticles.

Fire protection mainly takes place through physical or chemical pathways or both of them. The thermal diffusivity is one of the basic thermophysical properties which can connect the chemical structure. It is well-known in the literature that there exist relationships between the thermal diffusivity and the thermal stability. Also, the thermal diffusivity can be related to some fire retardant properties such as total-heat-release (THR), time-to-ignition (TTI) and peak-heat-rare-release (PHRR) that are of the most important parameters in the evaluation of potential fire hazard of a given material. Metal oxides, as one of the most promising flame retardant additives, improve the fire-retardant and the thermal stability properties of polymers. In the present study, molecular dynamic (MD) simulations based on the united atom model are utilized to study the effect of alumina nanoparticles on the thermal diffusivity of isotactic Polymethyl methacrylate (is-PMMA) polymer.