Collective Charge-density Excitations Research Articles

The Simple Generalized BCS-Type Model for the Acoustic Plasmon Induced d-Wave Superconductivity in High-Tc Layered Cuprate Compounds

A simple analytically treated model is presented for high-T c superconductivity in layered cuprate compounds. This model assumes a cylindrical Fermi-surface with circular cross-section, but anisotropic Fermi-velocity (density of states), which is approximated by a step-like function on azimuth angle. The system under these assumptions is shown to support in the long wavelength limit collective charge-density excitations with acoustic spectrum (acoustic plasmons), which suppress the Coulomb interelectron repulsion for small transferred momenta. This result leads to the second essential feature of the proposed model: besides the standard assumptions of the BCS scheme the effective potential of interelectron interaction is characterized by additional step-like dependence on the absolute value of two-dimensional transferred quasimomenta. The effective constants of the Cooper pairing in anisotropic s- and d-wave channels are evaluated. It is shown, that the plasmon mechanism gives rise to the pairing in the d-wave channel despite the fully isotropic (in two dimensions) model potential. The Umklapp processes are taken into account and are shown to increase the pairing constants.

Plasmons in Coupled Bilayer Structures

We calculate the collective charge density excitation dispersion and spectral weight in bilayer semiconductor structures {\it including effects of interlayer tunneling}. The out-of-phase plasmon mode (the ``acoustic'' plasmon) develops a long wavelength gap in the presence of tunneling with the gap being proportional to the square root (linear power) of the tunneling amplitude in the weak (strong) tunneling limit. The in-phase plasmon mode is qualitatively unaffected by tunneling. The predicted plasmon gap should be a useful tool for studying many-body effects.

Dynamical response of double parabolically graded quantum wells.

The collective charge-density excitations, the intra- and intersubband plasmons, and their manifestation in far-infrared transmission spectroscopy are studied for coupled quantum wells. We calculate self-consistently the ground state in the Hartree approximation and the density response in the random-phase approximation. We investigate the plasmons in symmetric coupled quantum wells in dependence on the coupling between the two wells and study the effects of deviation from the spatial symmetry. It is shown that the intersubband coupling forms a hybrid-type mode spectrum. The strong hybridization of the collective intrasubband motion with the lowest-frequency intersubband transition presses one branch in the single-particle intrasubband continuum and the higher-frequency intersubband modes form doublets. The optical transmission spectra of these samples with a grating coupler above the electron system show a strong exchange of oscillator strength between the modes. \textcopyright{} 1996 The American Physical Society.

Coupling of lateral and vertical electron motion in GaAs-AlxGa1-xAs quantum wires and dots.

Electronic excitations in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As-GaAs quantum wires and quantum dots have been investigated by means of resonant inelastic light scattering. At low frequencies, we find quasi-one-dimensional and quasi-zero-dimensional confined plasmons. Interestingly, we observe, at higher frequencies, not only the original two-dimensional (2D) intersubband excitations, but additional modes ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$ in polarized scattering geometry. The experimental finding is that the frequencies of these modes obey the relation ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}^{2}$\ensuremath{\approxeq}${\mathrm{\ensuremath{\omega}}}_{2\mathrm{D}}^{2}$+${\mathrm{\ensuremath{\omega}}}_{\mathrm{}1\mathrm{D}/0\mathrm{D}}^{2}$, where ${\mathrm{\ensuremath{\omega}}}_{2\mathrm{D}}$ is the frequency of the vertical intersubband charge-density excitation. ${\mathrm{\ensuremath{\omega}}}_{1\mathrm{D}}$ is a lateral quasi-one-dimensional confined plasmon frequency in wires and ${\mathrm{\ensuremath{\omega}}}_{0\mathrm{D}}$ is the frequency of a quasi-zero-dimensional confined plasmon in dots. This relation shows that the additional modes are collective charge-density excitations, which occur due to a coupling of lateral and vertical electron motion. \textcopyright{} 1996 The American Physical Society.

Bulk and surface plasmons in solids

In three-dimensional systems the dispersion of bulk plasmons in the electrostatic limit depends upon nonlocal effects in the conductivity or dielectric function. In addition to nonlocal effects, a non-abrupt surface electron density profile is necessary for the existence of higher multipole surface plasma modes. A spatially periodic bulk electron density gives rise to a band structure in the collective charge density excitation spectrum. For two-dimensional electron systems, like electrons confined to a narrow quantum well, the bulk 2D plasmon frequency is inversely proportional to the square root of the wavelength even in a simple local theory. Both regular and higher multipole edge modes can occur in the absence of nonlocal effects. For a periodic array of 2D electron layers, as in a superlattice, the collective charge density excitations can be classified as intrasubband and intersubband plasma modes. Each of these bands can support a surface plasma mode if the array of layers ends at a medium with different background dielectric constant than that containing the 2D electron layers. The basic concepts underlying the existence of all of these modes will be reviewed using the simplest models that contain the essential physics of the problem.

Collective excitations of a two-component one-dimensional quantum plasma confined in semiconductor quantum wires

The collective plasmon excitation spectrum of a one-dimensional electron gas confined in a GaAs quantum wire is calculated within the two-subband random-phase approximation. We calculate the collective-charge-density-excitation (CDE) dispersion assuming that both the ground and the first excited subband states are occupied by electrons. We find four different branches of CDE modes, two of which are intrasubband CDE's and the other two intersubband CDE's. The mode-coupling effect between them is investigated by introducing a parity-breaking asymmetry in the confinement potential. Our calculated mode dispersion is in excellent quantitative agreement with a recent inelastic-light-scattering experiment.

Interacting intersubband excitations in parabolic semiconductor quantum wells.

We calculate the finite wave-vector intersubband collective excitation spectra in wide parabolic wells at low two-dimensional electron densities where only the lowest quantum subband is occupied by electrons. We use a self-consistent time-dependent local-density approximation to calculate the linear response of the system, comparing our density-functional results with the noninteracting time-dependent Hartree approximation to estimate the magnitudes of exchange-correlation corrections to the collectivemode dispersion. We predict a qualitatively new phenomenon at low electron densities where, in the presence of exchange-correlation effects, it becomes possible for the collective charge-density excitation (i.e., the intersubband plasmon mode) to lie below the intersubband quasiparticle continuum

Many-body coupling between quasiparticle and collective excitations in semiconductor quantum wells.

We predict that, due to a many-body coupling between collective and single-particle excitations, there is an experimentally observable resonant line splitting in the intersubband collective charge-density excitation spectra in wide semiconductor quantum wells at low electron densities. This many-body coupling causes even the long-wavelength intersubband plasmon mode to be Landau damped at a critical density. Above the critical density, the intersubband plasmon mode lies [ital lower] in energy than the single-particle excitation.

Charge density excitations of two-dimensional magnetoplasma in semiconductor superlattices

This paper presents the theoretical investigation of collective charge density excitations in two-dimensional semiconductor superlattices subjected to a perpendicular magnetic field. We use a simple electromagnetic theory with a two-dimensional Dirac-δ function for the charge density profile. The magnetoplasmon dispersion relations are derived for an infinite and semi-infinite superlattices, both type II (InAs-GaSb systems) and type I (GaAs-AlxGa1−xAs systems). We emphasize on the magnetoplasma polaritons of semi-infinite superlattices. A detailed analytical diagnosis has been made of the dispersion relations to study the various limiting situations. The surface charge density excitations in the type II superlattices display a broken degeneracy in the retarded limit due to the presence of an applied magnetic field. This interestingly happens with the surface plasmon branch lying within the gap between two bulk bands. Moreover, the Q (Bloch wave vector)=0 edge of the bulk bands exhibits the splitting of the dispersion curve at a frequency (ω) greater than the cyclotron frequency (ωc). Application of a magnetic field results, in general, in pushing the whole spectrum lying above ω=ωc. The numerical results, including the retardation effects, both for zero and nonzero magnetic fields, have been presented for several illustrative cases.

Calculations of inelastic light scattering from surface plasmons with null critical wave vector in a metal-insulator semi-infinite superlattice.

The dispersion relation for collective charge-density excitations and the intensities of inelastic light scattering for intrasubband and intersubband transitions from a semi-infinite semiconductor superlattice topped with a metal-insulator layer are derived from a random-phase-approximation theory. Surface plasmons with null critical wave vector below the bulk plasmon band continuum are found. Calculations show that the spectral weight and the separation between the peaks of the surface and bulk plasmons are favorable for observation of surface plasmons in this system experimentally.

Surface plasmons in graphite intercalation compounds

Collective charge density excitations in a semi-infinite Graphite Intercalation Compounds are studied. The general theory is formulated and applied to intraband surface plasmons in stage 1 compound and interband surface plasmons in stage 2 compound. It is found that the surface plasmons can exist for the wavevector q larger than a critical value q ∗, in analogy with semiconductor superlattices. Analytical expressions are derived for plasmon frequency and decay length.

Inelastic light scattering by collective charge-density excitations in GaAs-Ga1-xAlxAs superlattices.

We consider the collective excitations of a finite GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As superlattice with arbitrary subband structure and electronic density. The density-density correlation function is calculated with use of the random-phase approximation, augmented by the local-density-functional theory. Exchange and correlation effects, self-consistent subband wave functions and energies, and intersubband scattering for arbitrary electron densities are taken into account. The resonant inelastic-light-scattering spectra by collective excitations are calculated. It is found that coupling between intersubband and intrasubband modes is very important when several subbands are occupied, in contrast to the results obtained with only a single subband occupied. The effects of exchange and correlation are found to be small.

Surface collective charge-density excitations of a semiconductor superlattice.

The surface of a semi-infinite semiconductor superlattice is specified by the angle theta between the surface and the superlattice axis. The dispersion relation of surface magnetoplasma modes is calculated for an arbitrary value of this angle. This work represents a generalization of the theory of the surface collective charge-density excitation of the lateral surface of a superlattice.

Bulk and Surface Plasmons in Artificially Structured Materials

The bulk and surface collective charge density excitations of metallic and semiconducting superlattice structures are studied. Because of the new periodicity along the axis of an infinite superlattice, these plasma modes form bands which satisfy Bloch's theorem. The dependence of the band structure on the material parameters is investigated. For finite or semi-infinite systems novel surface plasmons can occur. The coupling of the bulk and surface collective modes to external probes is reviewed.

Inelastic electron scattering by collective charge density excitations at the surface of a semiconductor superlattice

Inelastic electron scattering by collective charge density excitations at the surface of a semiconductor superlattice

Inelastic electron scattering by collective charge density excitations at the surface of a semiconductor superlattice

Using linear response theory and the diagonal approximation we calculate exactly and analytically surface response of a semi-infinite semiconductor superlattice to an electron moving in the vacuum. This response determines the scattering process. The electron energy loss spectrum due to surface intra- and intersubband plasmons is predicted for the first time.

Inelastic light scattering by collective charge-density excitations in semi-infinite semiconductor superlattices.

An analytic expression for the resonant, inelastic light scattering cross section from collective charge-density excitations of a semi-infinite semiconductor superlattice is derived. Raman intensities of bulk and surface modes of an n-type GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As sample are analyzed. Calculations show that intersubband surface plasmons have higher intensity than intrasubband ones and should be easier to observe experimentally. The line shapes of bulk spectra are explained in terms of photon broadening and broken translational symmetry in the superlattice direction. A new band of intersubband surface modes, with frequencies below the longitudinal-optical phonon frequency, is found.

Inelastic electron scattering by collective charge-density excitations at the surface of a semiconductor superlattice.

We have studied the oscillator strength of the lowest 1s heavy excitons in GaAs-AlAs quantum wells as a function of well-layer thickness by means of optical absorption. The oscillator strength of the lowest 1s heavy excitons is largely enhanced with the decrease of well-layer thickness. The result is the first full experimental observation of two-dimensional shrinkage of the exciton wave function in quantum wells.