Polarization Dependence of Raman Spectra in Strained Graphene

The polarization dependences of the G, D, and 2D (G$'$) bands in Raman spectra at graphene bulk and edge are examined theoretically. The 2D and D bands have different selection rules at bulk and edge. At bulk, the 2D band intensity is maximum when the polarization of the scattered light is parallel to that of incident light, whereas the D band intensity does not have a polarization dependence. At edge, the 2D and D bands exhibit a selection rule similar to that of the G band proposed in a previous paper. We suggest that a constraint equation on the axial velocity caused by the graphene edge is essential for the dependence of the G band on the crystallographic orientation observed in the bulk of strained graphene. This is indicative of that the pseudospin and valleyspin in the bulk of graphene can not be completely free from the effect of surrounding edge. The status of the experiments on the G and D bands at the graphene edge is mentioned.Comment: 11 pages, 3 figure

Berry's Phase for Standing Wave Near Graphene Edge

Standing waves near the zigzag and armchair edges, and their Berry's phases are investigated. It is suggested that the Berry's phase for the standing wave near the zigzag edge is trivial, while that near the armchair edge is non-trivial. A non-trivial Berry's phase implies the presence of a singularity in parameter space. We have confirmed that the Dirac singularity is absent (present) in the parameter space for the standing wave near the zigzag (armchair) edge. The absence of the Dirac singularity has a direct consequence in the local density of states near the zigzag edge. The transport properties of graphene nanoribbons observed by recent numerical simulations and experiments are discussed from the point of view of the Berry's phases for the standing waves.Comment: 6 pages, 4 figure

Ground state of graphite ribbons with zigzag edges

We study the interaction effects on the ground state of nanographite ribbons with zigzag edges. Within the mean-field approximation, we found that there are two possible phases: the superconducting (SC) phase and the excitonic insulator (EI). The two phases are separated by a first-order transition point. After taking into account the low-lying fluctuations around the mean-field solutions, the SC phase becomes a spin liquid phase with one gapless charge mode. On the other hand, all excitations in the EI phase, especially the spin excitations, are gapped.Comment: 6 pages, 3 figure

A tight lower bound for an online hypercube packing problem and bounds for prices of anarchy of a related game

We prove a tight lower bound on the asymptotic performance ratio $\rho$ of the bounded space online $d$-hypercube bin packing problem, solving an open question raised in 2005. In the classic $d$-hypercube bin packing problem, we are given a sequence of $d$-dimensional hypercubes and we have an unlimited number of bins, each of which is a $d$-dimensional unit hypercube. The goal is to pack (orthogonally) the given hypercubes into the minimum possible number of bins, in such a way that no two hypercubes in the same bin overlap. The bounded space online $d$-hypercube bin packing problem is a variant of the $d$-hypercube bin packing problem, in which the hypercubes arrive online and each one must be packed in an open bin without the knowledge of the next hypercubes. Moreover, at each moment, only a constant number of open bins are allowed (whenever a new bin is used, it is considered open, and it remains so until it is considered closed, in which case, it is not allowed to accept new hypercubes). Epstein and van Stee [SIAM J. Comput. 35 (2005), no. 2, 431-448] showed that $\rho$ is $\Omega(\log d)$ and $O(d/\log d)$, and conjectured that it is $\Theta(\log d)$. We show that $\rho$ is in fact $\Theta(d/\log d)$. To obtain this result, we elaborate on some ideas presented by those authors, and go one step further showing how to obtain better (offline) packings of certain special instances for which one knows how many bins any bounded space algorithm has to use. Our main contribution establishes the existence of such packings, for large enough $d$, using probabilistic arguments. Such packings also lead to lower bounds for the prices of anarchy of the selfish $d$-hypercube bin packing game. We present a lower bound of $\Omega(d/\log d)$ for the pure price of anarchy of this game, and we also give a lower bound of $\Omega(\log d)$ for its strong price of anarchy

Magnetic Correlations at Graphene Edges

Magnetic zigzag edges of graphene are considered as a basis for novel spintronics devices despite the fact that no true long-range magnetic order is possible in one dimension. We study the transverse and longitudinal fluctuations of magnetic moments at zigzag edges of graphene from first principles. We find a high value for the spin wave stiffness $D$ = 2100 meV \AA$^2$ and a spin-collinear domain wall creation energy $E_dw$ = 114 meV accompanied by low magnetic anisotropy. Above the crossover temperature $T_x \approx$10 K the spin correlation length $\xi \propto T^{-1}$ limits the long-range magnetic order to ~1 nm at 300 K while below $T_x$ it grows exponentially with decreasing temperature. We discuss possible ways of increasing the range of magnetic order and effects of edge roughness on it.Comment: 4 pages, 4 figure

Numerical study of the lattice vacancy effects on the single-channel electron transport of graphite ribbons

Lattice vacancy effects on electrical conductance of nanographite ribbon are investigated by means of the Landauer approach using a tight binding model. In the low-energy regime ribbons with zigzag boundary provide a single conducting channel whose origin is connected with the presence of edge states. It is found that the chemical potential dependence of conductance strongly depends on the difference ($\Delta$) of the number of removed A and B sublattice sites. The large lattice vacancy with $\Delta\neq 0$ shows $2\Delta$ zero-conductance dips in the single-channel region, however, the large lattice vacancy with $\Delta=0$ has no dip structure in this region. The connection between this conductance rule and the Longuet-Higgins conjecture is also discussed

Temperature Dependence of the Superfluid Density in a Noncentrosymmetric Superconductor

For a noncentrosymmetric superconductor such as CePt3Si, we consider a Cooper pairing model with a two-component order parameter composed of spin-singlet and spin-triplet pairing components. We calculate the superfluid density tensor in the clean limit on the basis of the quasiclassical theory of superconductivity. We demonstrate that such a pairing model accounts for an experimentally observed feature of the temperature dependence of the London penetration depth in CePt3Si, i.e., line-node-gap behavior at low temperatures.Comment: 10 page

Electronic States of Graphene Nanoribbons

We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively understood using the Dirac equation with appropriate boundary conditions. For the zigzag nanoribbon we demonstrate that the boundary condition allows a particle- and a hole-like band with evanescent wavefunctions confined to the surfaces, which continuously turn into the well-known zero energy surface states as the width gets large. For armchair edges, we show that the boundary condition leads to admixing of valley states, and the band structure is metallic when the width of the sample in lattice constant units is divisible by 3, and insulating otherwise. A comparison of the wavefunctions and energies from tight-binding calculations and solutions of the Dirac equations yields quantitative agreement for all but the narrowest ribbons.Comment: 5 pages, 6 figure

Chalker-Coddington model described by an S-matrix with odd dimensions

The Chalker-Coddington network model is often used to describe the transport properties of quantum Hall systems. By adding an extra channel to this model, we introduce an asymmetric model with profoundly different transport properties. We present a numerical analysis of these transport properties and consider the relevance for realistic systems.Comment: 7 pages, 4 figures. To appear in the EP2DS-17 proceeding