Impurity State and Variable Range Hopping Conduction in Graphene

The variable range hopping theory, as formulated for exponentially localized impurity states, does not necessarily apply in the case of graphene with covalently attached impurities. We analyze the localization of impurity states in graphene using the nearest-neighbor, tight-binding model of an adatom-graphene system with Green's function perturbation methods. The amplitude of the impurity state wave function is determined to decay as a power law with exponents depending on sublattice, direction, and the impurity species. We revisit the variable range hopping theory in view of this result and find that the conductivity depends as a power law of the temperature with an exponent related to the localization of the wave function. We show that this temperature dependence is in agreement with available experimental results

Bilayer graphene under pressure: Electron-hole Symmetry Breaking, Valley Hall Effect, and Landau Levels

The electronic structure of bilayer graphene under pressure develops very interesting features with an enhancement of the trigonal warping and a splitting of the parabolic touching bands at the K point of the reciprocal space into four Dirac cones, one at K and three along the T symmetry lines. As pressure is increased, these cones separate in reciprocal space and in energy, breaking the electron-hole symmetry. Due to their energy separation, their opposite Berry curvature can be observed in valley Hall effect experiments and in the structure of the Landau levels. Based on the electronic structure obtained by Density Functional Theory, we develop a low energy Hamiltonian that describes the effects of pressure on measurable quantities such as the Hall conductivity and the Landau levels of the system.Comment: 11 pages, 9 figure

Analysis of periodic Schrodinger operators: regularity and approximation of eigenfunctions.

Let V be a real valued potential that is smooth everywhere on R 3 , except at a periodic, discrete set S of points, where it has singularities of the Coulomb-type Z/r . We assume that the potential V is periodic with period lattice L . We study the spectrum of the Schrödinger operator H=−Δ+V acting on the space of Bloch waves with arbitrary, but fixed, wavevector k . Let T≔R 3 /L . Let u be an eigenfunction of H with eigenvalueλ and let ϵ>0 be arbitrarily small. We show that the classical regularity of the eigenfunction u is u∊H 5/2−ϵ (T) in the usual Sobolev spaces, and u∊K m 3/2−ϵ (T\S) in the weighted Sobolev spaces. The regularity index m can be as large as desired, which is crucial for numerical methods. For any choice of the Bloch wavevector k , we also show that H has compact resolvent and hence a complete eigenfunction expansion. The case of the hydrogen atom suggests that our regularity results are optimal. We present two applications to the numerical approximation of eigenvalues: using wave functions and using piecewise polynomials

Low energy phases of bilayer Bi predicted by structure search in two dimensions

We employ an ab-initio structure search algorithm to explore the configurational space of Bi in quasi two dimensions. A confinement potential restricts the movement of atoms within a pre-defined thickness during structure search calculations within the minima hopping method to find the stable and metastable forms of bilayer Bi. In addition to recovering the two known low-energy structures (puckered monoclinic and buckled hexagonal), our calculations predict three new structures of bilayer Bi. We call these structures the $\alpha$, $\beta$, and $\gamma$ phases of bilayer Bi, which are, respectively, 63, 72, and 83 meV/atom higher in energy than that of the monoclinic ground state, and thus potentially synthesizable using appropriate substrates. We also compare the structural, electronic, and vibrational properties of the different phases. The puckered monoclinic, buckled hexagonal, and $\beta$ phases exhibit a semiconducting energy gap, whereas $\alpha$ and $\gamma$ phases are metallic. We notice an unusual Mexican-hat type band dispersion leading to a van Hove singularity in the buckled hexagonal bilayer Bi. Notably, we find symmetry-protected topological Dirac points in the electronic spectrum of the $\gamma$ phase. The new structures suggest that bilayer Bi provides a novel playground to study distortion-mediated metal-insulator phase transitions

Photoluminescence from nanocrystalline graphite monofluoride

We synthesize and study the structural and optical properties of nanocrystalline graphene monofluoride and graphite monofluoride, which are carbon-based wide bandgap materials. Using laser excitations 2.41 - 5.08 eV, we identify six emission modes of graphite monofluoride, spanning the visible spectrum from red to violet. The energy and linewidth of the modes point to defect-induced midgap states as the source of the photoemission. We discuss possible candidates. Our findings open the window to electro-optical applications of graphene fluoride.Comment: 11 pages including supporting information, 2 figure

Metal-substituted Ti8C12 metallocarbohedrynes: toward less reactive clusters as building blocks of cluster-assembled materials

To form cluster-assembled materials, the clusters should have low reactivity and be characterized by a closed-shell electronic configuration with a large gap between the highest occupied and the lowest unoccupied molecular orbitals (HOMO-LUMO). Using spin-polarized density functional theory calculations, we investigate the M-substituted Ti8C12 metallocarbohedrynes to search for less reactive clusters as building blocks for cluster-assembled materials (M = Be, Mg, Ca, Sr, Ba and Sc, Y). The selected atoms in the correct stoichiometry would produce a metallocarbohedryne that is isoelectronic with the Ti8C122+, which has a closed-shell electronic configuration and an enhanced HOMO-LUMO gap of 1.735 eV. According to our results, the HOMO-LUMO gaps of the M-substituted Ti8C12 metallocarbohedrynes are in the range of 0.715-0.979 eV for the case of Be, Mg, Ca, Sr and Ba and in the range of 0.865-1.294 eV for the case of Sc and Y. Among all the M-substituted metallocarbohedrynes we consider here, one of the isomers of Ti6Sc2C12 is not only energetically more favorable but also exhibits a larger HOMO-LUMO gap of 1.294 eV. This result indicates that the Ti6Sc2C12(4) metallocarbohedryne should be less reactive than the Ti8C12 metallocarbohedryne which has a narrow HOMO-LUMO gap of 0.146 eV. Moreover, we show that the intercluster interaction between two individual Ti6Sc2C12(4) metallocarbohedrynes is relatively weak compared to the Ti8C12 dimer