Transverse electric plasmons in bilayer graphene

We predict the existence of transverse electric (TE) plasmons in bilayer graphene. We find that their plasmonic properties are much more pronounced in bilayer than in monolayer graphene, in a sense that they can get more localized at frequencies just below $\hbar\omega=0.4$~eV for adequate doping values. This is a consequence of the perfectly nested bands in bilayer graphene which are separated by $\sim 0.4$~eV

Screening effect on the optical absorption in graphene and metallic monolayers

Screening is one of the fundamental concepts in solid state physics. It has a great impact on the electronic properties of graphene where huge mobilities were observed in spite of the large concentration of charged impurities. While static screening has successfully explained DC mobilities, screening properties can be significantly changed at infrared or optical frequencies. In this paper we discuss the influence of dynamical screening on the optical absorption of graphene and other 2D electron systems like metallic monolayers. This research is motivated by recent experimental results which pointed out that graphene plasmon linewidths and optical scattering rates can be much larger than scattering rates determined by DC mobilities. Specifically we discuss a process where a photon incident on a graphene plane can excite a plasmon by scattering from an impurity, or surface optical phonon of the substrate.Comment: 19 pages, 2 figure

Many-hole interactions and the average lifetimes of chaotic transients that precede controlled periodic motion

We consider n small regions (referred to as the holes) on a chaotic attractor and study the average lifetime it takes for a randomly initiated trajectory to land in their union. The holes are thought of as n possible escape routes for the trajectory. The escape route through one of the holes may be considerably reduced by other holes, depending on their positions. This effect, referred to as shadowing, can significantly prolong the average lifetime. The main result of this paper is the construction and analysis (numerical and theoretical) of the many-hole interactions. They are interpreted as the amount of shadowing between the holes. The “effective range” of these interactions is associated with the largest Lyapunov exponent. The shadowing effect is shown to be very large when the holes are located on n points of an unstable periodic orbit. Considerable attention is paid to this case since it is of interest to the field of controlling chaos

Many-hole interactions and the average lifetimes of chaotic transients that precede controlled periodic motion

We consider n small regions (referred to as the holes) on a chaotic attractor and study the average lifetime it takes for a randomly initiated trajectory to land in their union. The holes are thought of as n possible escape routes for the trajectory. The escape route through one of the holes may be considerably reduced by other holes, depending on their positions. This effect, referred to as shadowing, can significantly prolong the average lifetime. The main result of this paper is the construction and analysis (numerical and theoretical) of the many-hole interactions. They are interpreted as the amount of shadowing between the holes. The “effective range” of these interactions is associated with the largest Lyapunov exponent. The shadowing effect is shown to be very large when the holes are located on n points of an unstable periodic orbit. Considerable attention is paid to this case since it is of interest to the field of controlling chaos

Naturally invariant measure of chaotic attractors and the conditionally invariant measure of embedded chaotic repellers

We study local and global correlations between the naturally invariant measure of a chaotic one-dimensional map f and the conditionally invariant measure of the transiently chaotic map f_H. The two maps differ only within a narrow interval H, while the two measures significantly differ within the images f^l(H), where l is smaller than some critical number l_c. We point out two different types of correlations. Typically, the critical number l_c is small. The χ^2 value, which characterizes the global discrepancy between the two measures, typically obeys a power-law dependence on the width ε of the interval H, with the exponent identical to the information dimension. If H is centered on an image of the critical point, then l_c increases indefinitely with the decrease of ε, and the χ^2 value obeys a modulated power-law dependence on ε

Theoretical and experimental analysis of a thin elastic cylindrical tube acting as a non-Hookean spring

We analyze the (large) deformation and energy of a thin elastic cylindrical tube compressed between two plates parallel to the tube axis. The deformation is studied theoretically using a numerical calculation and the variational approach. The results are used to interpret the experimental data obtained by pressing tubes made from plastic-foil transparencies.We obtain a universal scaling relation that characterizes the response of the tube. Our results may serve as a benchmark for the application of variational methods to thin-walled nanoscale systems in order to obtain functional relations between the energy and the deformation

Plasmonics in graphene at infra-red frequencies

We point out that plasmons in doped graphene simultaneously enable low-losses and significant wave localization for frequencies below that of the optical phonon branch $\hbar\omega_{Oph}\approx 0.2$ eV. Large plasmon losses occur in the interband regime (via excitation of electron-hole pairs), which can be pushed towards higher frequencies for higher doping values. For sufficiently large dopings, there is a bandwidth of frequencies from $\omega_{Oph}$ up to the interband threshold, where a plasmon decay channel via emission of an optical phonon together with an electron-hole pair is nonegligible. The calculation of losses is performed within the framework of a random-phase approximation and number conserving relaxation-time approximation. The measured DC relaxation-time serves as an input parameter characterizing collisions with impurities, whereas the contribution from optical phonons is estimated from the influence of the electron-phonon coupling on the optical conductivity. Optical properties of plasmons in graphene are in many relevant aspects similar to optical properties of surface plasmons propagating on dielectric-metal interface, which have been drawing a lot of interest lately because of their importance for nanophotonics. Therefore, the fact that plasmons in graphene could have low losses for certain frequencies makes them potentially interesting for nanophotonic applications.Comment: 5 figure

Breakdown of Dirac Dynamics in Honeycomb Lattices due to Nonlinear Interactions

We study the dynamics of coherent waves in nonlinear honeycomb lattices and show that nonlinearity breaks down the Dirac dynamics. As an example, we demonstrate that even a weak nonlinearity has major qualitative effects one of the hallmarks of honeycomb lattices: conical diffraction. Under linear conditions, a circular input wave-packet associated with the Dirac point evolves into a ring, but even a weak nonlinearity alters the evolution such that the emerging beam possesses triangular symmetry, and populates Bloch modes outside of the Dirac cone region. Our results are presented in the context of optics, but we propose a scheme to observe equivalent phenomena in Bose-Einstein condensates

The Quantum Hall Effect with Wilczek's charged magnetic flux tubes instead of electrons

Composites formed from charged particles and magnetic flux tubes, proposed by Wilczek, are one model for anyons - particles obeying fractional statistics. Here we propose a scheme for realizing charged flux tubes, in which a charged object with an intrinsic magnetic dipole moment is placed between two semi-infinite blocks of a high permeability ($\mu_r$) material, and the images of the magnetic moment create an effective flux tube. We show that the scheme can lead to a realization of Wilczek's anyons, when a two-dimensional electron system, which exhibits the integer quantum Hall effect (IQHE), is sandwiched between two blocks of the high-$\mu_r$ material with a temporally fast response (in the cyclotron and Larmor frequency range). The signature of Wilczek's anyons is a slight shift of the resistivity at the plateau of the IQHE. Thus, the quest for high-$\mu_r$ materials at high frequencies, which is underway in the field of metamaterials, and the quest for anyons, are here found to be on the same avenue.Comment: are welcom