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We have investigated the α–T3 model in the presence of a mass term which opens a gap in the energy dispersive spectrum, as well as under a uniform perpendicular quantizing magnetic field. The gap opening mass term plays the role of Zeeman splitting at low magnetic fields for this pseudospin-1 system, and, as a consequence, we are able to compare physical properties of the the α–T3 model at low and high magnetic fields. Specifically, we explore the magnetoplasmon dispersion relation in these two extreme limits. Central to the calculation of these collective modes is the dielectric function which is determined by the polarizability of the system. This latter function is generated by transition energies between subband states, as well as the overlap of their wave functions.

We compare the two-dimensional (2D) plasmon dispersion relations for monolayer graphene when the sample is doped with carriers in the conduction band and the temperature $T$ is zero with the case when the temperature is finite and there is no doping. Additionally, we have obtained the plasmon excitations when there is doping at finite temperature. The results were obtained in the random-phase approximation which employs energy electronic bands calculated using ab initio density functional theory. We found that in the undoped case the finite temperature results in appearance in the low-energy region of a 2D plasmon which is absent for the $T=0$ case. Its energy is gradually increased with increasing $T$. It is accompanied by expansion in the momentum range where this mode is observed as well. The 2D plasmon dispersion in the $\Gamma$M direction may differ in substantial ways from that along the $\Gamma$K direction at sufficiently high temperature and doping concentrations. Moreover, at temperatures exceeding $\approx300$ meV a second mode emerges along the $\Gamma$K direction at lower energies like it occurs at a doping level exceeding $\approx 300$ meV. Once the temperature exceeds $\approx 0.75$ eV this mode ceases to exit whereas the 2D plasmon exists as a well-defined collective excitation up to $T=1.5$ eV, a maximal temperature investigated in this work., Comment: 11 pages, 8 figures

We present a description of the energy loss of a charged particle moving parallel to a graphene layer and graphene double layers. Specifically, we compare the stopping power of the plasma oscillations for these two configurations in the absence as well as the presence of circularly polarized light whose frequency and intensity can be varied to yield an energy gap of several hundred $\texttt{meV}$ between the valence and conduction bands. The dressed states of the Dirac electrons by the photons yield collective plasma excitations whose characteristics are qualitatively and quantitatively different from those produced by Dirac fermions in gapless graphene, due in part to the finite effective mass of the dressed electrons. For example, the range of wave numbers for undamped self-sustaining plasmons is increased as the gap is increased, thereby increasing the stopping power of graphene for some range of charged particle velocity when graphene is radiated by circularly polarized light.

The presence of several kinds of carriers at the Fermi surface results in interesting complex dielectric properties of the bulk Pd in the low-energy excitation range. A most spectacular manifestation of this is the presence of a collective electronic excitation characterized by a soundlike dispersion, termed acoustic plasmon (AP). Due to the characteristic dispersion reaching zero energy in the long-wavelength limit, the question of the thermal stability of the excitation spectrum arises. In this work we explore this problem investigating the thermal effect on the electronic excitation spectrum in this material, tracing how the AP properties vary with the temperature increase. The main effect consists in the gradual destruction of AP in the energy range corresponding to the temperature., V.M.S. and E.V.C. acknowledge partial support from the University of the Basque Country, Grant No. IT-756-13, and the Spanish Ministry of Economy and Competitiveness MINECO, Grant No. FIS2013-48286-C2-1-P. V.U.N. acknowledges support from the Ministry of Science and Technology, Taiwan, Grants No. 104-2112-M-001-007 and No. 105-2112-M-001-010.

We calculate the exact time-dependent single-particle eigenstates for electrons in an intense terahertz laser field applied along the axis of a cylindrical nanotube. Making use of these results and linear-response theory, we obtain the charge density fluctuations for an interacting electron gas confined to the surface of the nanotube. The dispersion equation for the collective plasmon-polariton excitations is derived. Numerical results are presented for the dispersion relation as a function of the wave vector along the axis of the nanotube.

We perform a comprehensive analysis of the spectrum of graphene plasmons which arise when a pair of sheets are confined between conducting materials. The associated enhanced local fields may be employed in the manipulation of light on the nanoscale by adjusting the separation between the graphene layers, the energy band gap as well as the concentration of charge carriers in the conducting media surrounding the two-dimensional (2D) layers. We present a theoretical formalism, based on the calculation of the surface response function, for determining the plasmon spectrum of an encapsulated pair of 2D layers and apply it to graphene. We solve the coupled equations involving the continuity of the electric potential and discontinuity of the electric field at the interfaces separating the constituents of the hybrid structure. We have compared the plasmon modes for encapsulated gapped and gapless graphene. The associated nonlocal graphene plasmon spectrum coupled to the “sandwich” system show a linear acoustic plasmon mode as well as a low-frequency mode corresponding to in-phase oscillations of the adjacent 2D charge densities. These calculations are relevant to the study of energy transfer via plasmon excitations when graphene is confined by a pair of thick conducting materials.

We have discovered a novel feature in the plasmon excitations for a pair of Coulomb-coupled non-concentric spherical two-dimensional electron gases (S2DEGs). Our results show that the plasmon excitations for such pairs depend on the orientation with respect to the external electromagnetic probe field. The origin of this anisotropy of the inter-sphere Coulomb interaction is due to the directional asymmetry of the electrostatic coupling of electrons in excited states which depend on both the angular momentum quantum number L and its projection M on the axis of quantization taken as the probe E-field direction. We demonstrate the anisotropic inter-sphere Coulomb coupling in space and present semi-analytic results in the random-phase approximation both perpendicular and parallel to the axis of quantization. For the incidence of light with a finite orbital or spin angular momentum, the magnetic field generated from an induced oscillating electric dipole on one sphere can couple to an induced magnetic dipole on another sphere in a way that is dependent on whether the direction is parallel or perpendicular to the probe E field. Such an effect from the plasmon spatial correlation is expected to be experimentally observable by employing circularly polarized light or a helical light beam for incidence. The S2DEG serves as a simple model for fullerenes as well as metallic dimers, when the energy bands are far apart.

A theory for the collective plasma excitations in a linear periodic array of spherical two-dimensional electron gases (S2DEGs) is presented. This is a simple model for an ultra thin and narrow microribbon of fullerenes or metallic shells. Coulomb coupling between electrons located on the same sphere and on different spheres is included in the random-phase approximation (RPA). Electron hopping between spheres is neglected in these calculations. The resulting plasmon-dispersion equation is solved numerically. Results are presented for a superlattice of single-wall S2DEGs as a function of the wave vector. The plasmon dispersions are obtained for different spherical separations. We show that the one-dimensional translational symmetry of the lattice is maintained in the plasmon spectrum. Additionally, we compare the plasmon dispersion when the superlatice direction is parallel or perpendicular to the axis of quantization. However, because of anisotropy in the Coulomb matrix elements, there is anticrossing in the plasmon dispersion only in the direction perpendicular to the quantization axis. The S2DEG may serve as a simple model for fullerenes, when their energy bands are far apart.

We present a formalism for calculating the absorption coefficient of a pair of coaxial tubules. A spatially nonlocal, dynamical self-consistent field theory is obtained by calculating the electrostatic potential produced by the charge density fluctuations as well as the external electric field. There are peaks in the absorption spectrum arising from plasma excitations corresponding either to plasmon or particle-hole modes. In this Letter, we numerically calculate the plasmon contribution to the absorption spectrum when an external electric field is applied. The number of peaks depends on the radius of the inner as well as outer tubule. The height of each peak is determined by the plasmon wavelength and energy. For a chosen wave number, the most energetic plasmon has the highest peak corresponding to the largest oscillator strength of the excited modes. Some of the low-frequency plasmon modes have such weak coupling to an external electric field that they are not seen on the same scale as the modes with larger energy of excitation. We plot the peak positions of the plasmon excitations for a pair of coaxial tubules. The coupled modes on the two tubules are split by the Coulomb interaction. The energies of the two highest plasmon branches increase with the radius of the outer tubule. On the contrary, the lowest modes decrease in energy as this radius is increased. No effects due to inter-tubule hopping are included in these calculations.

We have investigated the conditions necessary to achieve stronger Cherenkov-like instability of plasma waves leading to emission in the terahertz (THz) regime for semiconductor quantum wells (QWs). The surface response function is calculated for a bilayer two-dimensional electron gas (2DEG) system in the presence of a periodic spatial modulation of the equilibrium electron density. The 2DEG layers are coupled to surface plasmons arising from excitations of free carriers in the bulk region between the layers. A current is passed through one of the layers and is characterized by a drift velocity for the driven electric charge. By means of a surface response function formalism, the plasmon dispersion equation is obtained as a function of angular frequency, the in-plane wave vector and reciprocal lattice vector of the density modulation. The dispersion equation,is solved numerically in the complex frequency plane for real wave vector. It is ascertained that the imaginary part of the angular frequency is enhanced with decreasing period of modulation, and with increasing the doping density of the free carriers in the bulk medium for fixed period of the spatial modulation.

We calculate the plasma excitations in a bundle as well as a two-dimensional (2D) periodic array of aligned parallel multishell nanotubes on a substrate. The carbon nanotubes are oriented perpendicular to the substrate. The model we use for the system is an electron gas confined to the surface of an infinitely long cylinder embedded in a background dielectric medium. Electron tunneling between individual tubules is neglected. We include the Coulomb interaction between electrons on the same tubule and on different tubules for the same nanotube and neighboring nanotubes. We present a self-consistent field theory for the dispersion equation for intrasubband and intersubband plasmon excitations. For both the bundle and 2D array of aligned parallel nanotubes, the dispersion relation of the collective modes is determined by a three-dimensional wave vector with components in the direction of the nanotube axes and in the transverse directions. The dispersion equation is solved numerically for a single-wall nanotube 2D array as well as a bundle, and the plasmon excitation energies are obtained as a function of wave vector. The intertube Coulomb interaction couples plasmons with different angular momenta $m$ in individual nanotubes, lifting the $\ifmmode\pm\else\textpm\fi{}m$ degeneracy of the single-nanotube modes. This effect is analyzed numerically as a function of the separation between the tubules. We show that the translational symmetry of the lattice is maintained in the plasmon spectrum for the periodic array, and the plasmon energies have a periodic dependence on the transverse wave vector ${\mathbf{q}}_{\ensuremath{\perp}}$. For the bundle, the Coulomb interaction between nanotubes gives rise to optical plasmon excitations.

We have formulated a theory to help us investigate the conditions which are needed to achieve stronger plasmon instability leading to emission in the terahertz (THz) regime for semiconductor quantum wells (QWs). The surface response function is calculated for a bilayer two-dimensional electron gas (2DEG) system in the presence of a metal grating placed on the surface which modulates the electron density. The 2DEG layers are coupled to surface plasmons arising from excitations of free carriers in the bulk region between the layers. A current is passed through one of the 2DEG layers and is characterized by a drift velocity υ D . With the use of the surface response function, the plasmon dispersion equation is obtained as a function of frequency ω, the in-plane wave vector q ll = ( q x , q y ) and reciprocal lattice vector nG where n = 0,±1,±2, ... with G = 2π/ d and d denoting the period of the grating. The dispersion equation, which yields the resonant frequencies, is solved in the complex ω-plane for real wave vector q ll . It is ascertained that the imaginary part of ω is enhanced with decreasing d , and with increasing the doping density of the free carriers in the bulk medium for fixed grating period.

Carbon nanotubes have come under intense theoretical and experimental investigation focused on both their transport and photonic properties. Of recent interest is the observation that when a gate voltage is applied perpendicular to the axis of the nanotube, it can lead to spin-orbit interaction (SOI). This is of the same nature as the Rashba-Bychkov SOI at an asymmetric semiconductor heterojunction. We have calculated the "band states" for a cylindrical nanotube in the presence of SOI and then used the results to determine the collective plasma oscillations corresponding to electron transitions between the spin-split subbands for single-wall and multiwall nanotubes. These collective plasma modes determine the peak positions for the intersubband absorption coefficient as well as the energy loss spectrum. We show that the plasmon excitations for coaxial tubules have a region of instability which could lead to amplification in the energy transfer spectrum. The frequency regime where this instability occurs could be in the terahertz range. This source of radiation may be suitable for use in space-based detectors because of the durability and robustnes of carbon nanotubes.

We present a formalism for the rate of transfer of energy from a current of charged particles to multiwall and a linear array of nanotubes. The method is based on a self-consistent field theory involving Laplace's equation for the total screened potential and the density fluctuations on the nanotubes. It is demonstrated that one can identify the plasmon excitations from the spectrum of energy transfer. For a group of the excited plasmons, there is an instability associated with their decay. This occurrence is determined by the relationship between the phase velocity of the plasmon and the drift velocity of the current. A ``dip'' in the energy transfer spectrum corresponds to a plasmon mode instability. This is confirmed by solving the plasma dispersion equation in the complex frequency plane.

We develop a theory of collective plasma excitations in a pair of parallel nonoverlapping cylindrical nanotubes. A general dispersion equation is obtained as a function of the angular momentum and linear momentum transfer. We use our results to calculate the phase velocity of the plasmon excitations when current flows parallel to the axis of the nanotube in either the same or neighboring nanotube as the plasma excitations. We demonstrate that the less energetic undamped plasmon excitations may have a phase velocity which is smaller than the Fermi velocity. The plasmons with the largest frequencies have phase velocities which decrease with increasing wave vector. We discuss the instabilities which may arise when the drift velocity of the electrons lies within a range which is determined by the phase velocity for the plasmon modes of the pair of cylindrical nanotubes.