Dielectric function and plasmons in graphene

The electromagnetic response of graphene, expressed by the dielectric function, and the spectrum of collective excitations are studied as a function of wave vector and frequency. Our calculation is based on the full band structure, calculated within the tight-binding approximation. As a result, we find plasmons whose dispersion is similar to that obtained in the single-valley approximation by Dirac fermions. In contrast to the latter, however, we find a stronger damping of the plasmon modes due to inter-band absorption. Our calculation also reveals effects due to deviations from the linear Dirac spectrum as we increase the Fermi energy, indicating an anisotropic behavior with respect to the wave vector of the external electromagnetic field

Dynamical polarization, screening, and plasmons in gapped graphene

The one-loop polarization function of graphene has been calculated at zero temperature for arbitrary wavevector, frequency, chemical potential (doping), and band gap. The result is expressed in terms of elementary functions and is used to find the dispersion of the plasmon mode and the static screening within the random phase approximation. At long wavelengths the usual square root behaviour of plasmon spectra for two-dimensional (2D) systems is obtained. The presence of a small (compared to a chemical potential) gap leads to the appearance of a new undamped plasmon mode. At greater values of the gap this mode merges with the long-wavelength one, and vanishes when the Fermi level enters the gap. The screening of charged impurities at large distances differs from that in gapless graphene by slower decay of Friedel oscillations ($1/r^2$ instead of $1/r^3$), similarly to conventional 2D systems.Comment: 8 pages, 8 figures, v2: to match published versio

Double Quantum Dots in Carbon Nanotubes

We study the two-electron eigenspectrum of a carbon-nanotube double quantum dot with spin-orbit coupling. Exact calculation are combined with a simple model to provide an intuitive and accurate description of single-particle and interaction effects. For symmetric dots and weak magnetic fields, the two-electron ground state is antisymmetric in the spin-valley degree of freedom and is not a pure spin-singlet state. When double occupation of one dot is favored by increasing the detuning between the dots, the Coulomb interaction causes strong correlation effects realized by higher orbital-level mixing. Changes in the double-dot configuration affect the relative strength of the electron-electron interactions and can lead to different ground state transitions. In particular, they can favor a ferromagnetic ground state both in spin and valley degrees of freedom. The strong suppression of the energy gap can cause the disappearance of the Pauli blockade in transport experiments and thereby can also limit the stability of spin-qubits in quantum information proposals. Our analysis is generalized to an array of coupled dots which is expected to exhibit rich many-body behavior.Comment: 14 pages, 11 pages and 1 table. Typos in text and Figs.4 and 6 correcte

Electron-electron interaction and charging effects in graphene quantum dots

We analyze charging effects in graphene quantum dots. Using a simple model, we show that, when the Fermi level is far from the neutrality point, charging effects lead to a shift in the electrostatic potential and the dot shows standard Coulomb blockade features. Near the neutrality point, surface states are partially occupied and the Coulomb interaction leads to a strongly correlated ground state which can be approximated by either a Wigner crystal or a Laughlin like wave function. The existence of strong correlations modify the transport properties which show non equilibrium effects, similar to those predicted for tunneling into other strongly correlated systems.Comment: Extended version accepted for publication at Phys. Rev.

Dielectric function of the semiconductor hole gas

We study the dielectric function of the homogeneous hole gas in p-doped zinc-blende III-V bulk semiconductors within random phase approximation with the valence band being modeled by Luttinger's Hamiltonian in the spherical approximation. In the static limit we find a beating of Friedel oscillations between the two Fermi momenta for heavy and light holes, while at large frequencies dramatic corrections to the plasmon dispersion occur.Comment: 4 pages, 1 figure included. Version to appear in Europhys. Let

Casimir interactions in graphene systems

The non-retarded Casimir interaction (van der Waals interaction) between two free standing graphene sheets as well as between a graphene sheet and a substrate is determined. An exact analytical expression is given for the dielectric function of graphene along the imaginary frequency axis within the random phase approximation for arbitrary frequency, wave vector, and doping.Comment: 4 pages, 4 figure

Re-entrant Nematic Phase Established for Several Homologous Biaromatic Liquid Crystals by Investigation of Binary Mixed Systems

Several homologous series of biaromatic liquid crystals with structure type CnH2n+1O • C6H4 • M•C6H4-CN are investigated. By studying the phase transition temperatures in binary mixed systems a "re-entrant" nematic phase N(re) is established for all compounds exhibiting smectic A phases. The virtual transition temperatures N(re) - SA are found to decrease with increasing chain length of the alkyloxy group. The influence of the middle group M on the re-entrant behaviour can be attributed mainly to its dipole moment. The temperature range of the smectic A phase decreases when the middle group dipole moment is additive to that of the nitrile group. To summarize it can be said that the "re-entrant" behaviour of biaromatic liquid crystals is found to be very similar to that of triaromatic systems reported recently

Coulomb Screening of 2D Massive Dirac Fermions

A model of 2D massive Dirac fermions, interacting with a instantaneous $1/r$ Coulomb interaction, is presented to mimic the physics of gapped graphene. The static polarization function is calculated explicitly to analyze screening effect at the finite temperature and density. Results are compared with the massless case . We also show that various other works can be reproduced within our model in a straightforward and unified manner

Comparison of Heuristic Dynamic Programming and Dual Heuristic Programming Adaptive Critics for Neurocontrol of a Turbogenerator

This paper presents the design of an optimal neurocontroller that replaces the conventional automatic voltage regulator (AVR) and the turbine governor for a turbogenerator connected to the power grid. The neurocontroller design uses a novel technique based on the adaptive critic designs (ACDs), specifically on heuristic dynamic programming (HDP) and dual heuristic programming (DHP). Results show that both neurocontrollers are robust, but that DHP outperforms HDP or conventional controllers, especially when the system conditions and configuration change. This paper also shows how to design optimal neurocontrollers for nonlinear systems, such as turbogenerators, without having to do continually online training of the neural networks, thus avoiding risks of instability

Few-body bound states in dipolar gases and their detection

We consider dipolar interactions between heteronuclear molecules in a low-dimensional setup consisting of two one-dimensional tubes. We demonstrate that attraction between molecules in different tubes can overcome intratube repulsion and complexes with several molecules in the same tube are stable. In situ detection schemes of the few-body complexes are proposed. We discuss extensions to the case of many tubes and layers, and outline the implications of our results on many-body physics.Comment: Published versio