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The interaction energy of the indirect-exchange or Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic spins localized on lattice sites of the $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}_{3}$ model is calculated using linear response theory. In this model, the AB-honeycomb lattice structure is supplemented with C atoms at the centers of the hexagonal lattice. This introduces a parameter $\ensuremath{\alpha}$ for the ratio of the hopping integral from hub to rim and that around the rim of the hexagonal lattice. A valley and $\ensuremath{\alpha}$-dependent retarded Green's function matrix is used to form the susceptibility. Analytic and numerical results are obtained for undoped $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}_{3}$ when the chemical potential is finite and also in the presence of an applied magnetic field. We demonstrate the anisotropy of these results when the magnetic impurities are placed on the A, B, and C sublattice sites. Additionally, a comparison of the behavior of the susceptibility of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}_{3}$ with graphene shows that there is a phase transition at $\ensuremath{\alpha}=0$.

Using the $\alpha-T_3$ model, we carried out analytical and numerical calculations for the static and dynamic polarization functions in the presence of a perpendicular magnetic field. The model involves a parameter $\alpha$ which is the ratio of the hopping strength from an atom at the center of a honeycomb lattice to one of the atoms on the hexagon to the hopping strength around its rim. Our results were employed to determine the longitudinal dielectric function and the magnetoplasmon dispersion relation. The magnetic field splits the continuous valence, conduction and at energy subband into discrete Landau levels which present significant effects on the polarization function and magnetoplasmon dispersion. This includes the fact that the energies of the Landau levels are valley dependent which leads to different behaviors of the polarization function as the hopping parameter $\alpha$ (or $\phi = tan^{-1}\alpha$) is reduced continuously toward zero. This essential critical behavior of the polarization function leads to a softening of a magnetoplasmon mode. We present results for a doped layer in the integer quantum Hall regime for fixed hopping parameter $\alpha$ and various magnetic fields as well as chosen magnetic field and different $\alpha$ in the random phase approximation.

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 formalism for calculating the image potential for a two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction (SOI) as well as for a 2D topological insulator (TI). The formalism is further generalized for including the Coulomb coupled multiple layers. Roles of broken inversion symmetry near the surface and the dielectric environment are investigated by using a surface-response function. The insignificant role of SOI in 2DEG is dramatically enhanced in TI by selecting a small relative permittivity $\epsilon_b$ for the dielectric environment. Manipulating $\epsilon_b$ is proven to provide an efficient way to drive electrons with opposite spins into two different integral quantum Hall states. The prediction made in this paper is expected to be experimentally observable for a 2DTI system, such as Bi$_2$Se$_3$, with a helical spin behavior and a dominant linear Rashba SOI-like term in the energy dispersion.

We compute and compare the effects due to a uniform perpendicular magnetic field as well as temperature on the static polarization functions for monolayer graphene (MLG), associated with the Dirac point, with that for the two-dimensional electron liquid (2DEL) with the use of comprehensive numerical calculations. The relevance of our study to the Friedel oscillations for the screening of the potential for a dilute distribution of impurities is reported too. Our results show substantial differences due to screening for the 2DEL and MLG which have not been given adequate attention previously.

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 investigated the effect due to perpendicular magnetic field on quantum wires where spin-orbit interaction (SOI) of electrons is not neglected. Based on the calculated energy dispersion, the nonlinear ballistic conductance ($G$) and electron-diffusion thermoelectric power ($S_d$) are calculated as functions of electron density, temperature and applied bias voltage. A low-temperature half-step feature in $G$, which was observed experimentally by Quay et al. [see Nature Physics {\bf 6}, 336 (2010)], as well as a new peak in $S_d$ are reproduced here in the low density regime. These phenomena are related to the occurrence of the Zeeman splitting and SOI induced saddle point in the band structure, where the channel chemical potential lies within an anticrossing gap between the saddle point of the lower subband and the bottom of the upper subband. Additionally, side peaks in $G$ far away from the zero bias for the nonlinear transport, as well as a quadratic bias-voltage dependence of $G$ near zero voltage, are predicted and discussed., 7 figures

We calculated the effects of spin-orbit interaction (SOI) on the energy bands, ballistic conductance and the electron-diffusion thermoelectric power of a nanowire by varying the temperature, electron density and width of the wire. The potential barriers at the edges of the wire are assumed to be very high. A consequence of the boundary conditions used in this model is determined by the energy band structure, resulting in wider plateaus when the electron density is increased due to larger energy-level separation as the higher subbands are occupied by electrons. The nonlinear dependence of the transverse confinement on position with respect to the well center excludes the "pole-like feature" in the conductance which is obtained when a harmonic potential is employed for confinement. At low temperature, the electron diffusion thermoelectric power increases linearly with T but deviates from the linear behavior for large values of T., Comment: Updated corrected version of the original submission

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 present ab initio time-dependent density-functional theory calculation results for low-energy collective electron excitations in ${\text{MgB}}_{2}$. The existence of a long-lived collective excitation corresponding to coherent charge density fluctuations between the boron $\ensuremath{\sigma}$ and $\ensuremath{\pi}$ bands ($\ensuremath{\sigma}\ensuremath{\pi}$ mode) is demonstrated. This mode has a sine-like oscillating dispersion for energies below 0.5 eV. At even lower energy we find another collective mode ($\ensuremath{\sigma}\ensuremath{\sigma}$ mode). We show the strong impact of local-field effects on dielectric functions in ${\text{MgB}}_{2}$. These effects account for the long $q$-range behavior of the modes. We discuss the physics that these collective excitations bring to the energy region typical for lattice vibrations.

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.

An experimental and theoretical study of electronic excitations in MgB2 covering the domain of large energy and momentum transfers is reported. Energy-loss spectra for several values of momentum transfers were measured in a polycrystalline sample by means of inelastic X-ray scattering spectroscopy. Ab initio calculations of the dielectric function as well as the energy-loss function were performed in the frame of the time-dependent local density approximation with inclusion of crystal local-field effects. We obtained very good agreement between the experimental and the theoretical energy dispersion of the peak maximum of the loss function. We found that crystal local-field effects are responsible for this agreement at large momenta. Fine structure observed in the measured spectra was interpreted in terms of strong interband transitions predicted by the calculations in the and directions. The theoretical dispersion of these features is in good accordance with the experimental data. Further spectral features in the measured spectra due to Mg 2s and 2p core electron excitations are also discussed., Financial support from SeCyT (Universidad Nacional de Córdoba, Argentina) and FAPESP and CNPq (Brazil) is gratefully acknowledged. The San Sebastián team acknowledges the partial support from the University of the Basque Country (Grant No. GIC07IT36607), Departamento de Educación del Gobierno Vasco, and the Spanish Ministerio de Ciencia y Technología (MCyT) (Grant No. FIS200766711C0101). The work of V.M.S. is sponsored by the IKERBASQUE Foundation. The research was supported by LNLS-Brazilian Synchrotron Light Laboratory/MCT.

We report on the results of calculation of low-energy dielectric response and optical properties of MgB2. The calculations have been performed with full inclusion of the ab initio electron band structure making use of random-phase and time-dependent local-density approximations. The role of local-field and exchange-correlation effects in MgB2 dielectric function is thoroughly examined. Index of refraction, extinction coefficient, and normal-incidence reflectivity exhibiting strong anisotropy were calculated for electromagnetic waves polarized along the a∗ and c∗ axes by using the evaluated electron-density-response functions. Our results are in good agreement with recent x-ray and optical measurements performed on MgB2 single crystals., We acknowledge the partial support from the University of the Basque Country Grant No. GIC07IT36607, the Departamento de Educación del Gobierno Vasco, and the Spanish Ministerio de Ciencia y Tecnología MCyT Grant No.FIS200766711C0101. The work of V.M.S. is sponsored by the IKERBASQUE Foundation.

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 calculate the image potential between the walls of a double-walled cylindrical nanotube which is assumed to be infinitely long. In this model, each tubule is infinitesimally thin and is embedded in a background dielectric medium. Interactions between electrons confined to move on the surface of each tubule are taken into account via the random-phase approximation. We demonstrate that the effective potential for an orbiting charge depends on its angular momentum as well as the separation between the tubules. We calculate the plasmon frequencies and their phase velocities as functions of the wave vector parallel to the axes of the tubules. The range for the drift velocity for current-driven plasma instabilities is discussed.

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.