2D Plasmons Research Articles

Theory of minigap plasmons in a two-dimensional electron gas subjected to a one-dimensional periodic potential

We investigate the plasmon excitations in a two-dimensional (2D) electron gas subjected to a one-dimensional (1D) weak periodic potential. We derive and discuss the dispersion relations for both intrasubband and intersubband excitations within the framework of Bohm-Pines' random-phase approximation. For such an anisotropic system with spatially modulated charge density, we observe a splitting of the 2D plasmon dispersion. The splitting is caused by the superlattice effect of the charge-density modulation on the collective excitation spectrum. Several illustrative examples are presented on the computed plasmon excitation energy as a function of the propagation vector as well as the Bloch vector. We also discuss how the tunneling and the potential amplitude influence the minigaps and the plasmon excitations.

Minigap plasmons in a two-dimensional electron gas subjected to a one-dimensional periodic potential

We investigate the plasmon excitations in a two-dimensional electron gas subjected to a one-dimensional weak periodic potential. We derive and discuss the dispersion relations for both intrasubband and intersubband excitations within the framework of Bohm–Pines' random-phase approximation. For such an anisotropic system with spatially modulated charge density, we observe a splitting of the 2D plasmon dispersion. The splitting is caused by the superlattice effect of the charge-density modulation on the collective excitation spectrum. We also discuss how the tunneling and the potential amplitude affect the plasmon excitations.

The Role of screening in the strongly correlated 2D systems

We investigate recently observed experiments in the strongly correlated 2D systems (rs 1) (low-density 2D plasmons, metallic behaviour of 2D systems and frictional drag resistivity between two 2D hole layers). We compare them with our theoretical results calculated within a conventional Fermi liquid theory with RPA screening.

Interaction, damping and possible amplification of 2D plasmons in asymmetric bilayer structures

It is shown that the asymmetry of a double quantum well structure considerably affects the dispersion relations for the optical and intersubband plasmons. A specific mechanism of the plasmon damping arises due to a resonance of the plasmon energy and that of single-particle intersubband transitions. If the population of the subbands is inverted, an amplification of the plasma waves becomes possible.

Two-dimensional plasmon in a metallic monolayer on a semiconductor surface: Exchange-correlation effects

Taking account of exchange-correlation (XC) effects, we investigate two-dimensional (2D) plasmons (PL's) in a metallic monolayer on a semiconductor surface. The energy dispersion and the energy-loss intensity of the 2D PL are calculated in close relation to a recent experiment by high-resolution electron energy-loss spectroscopy. We evaluate the XC effects by using the local-field-correction theory and by comparing the calculated results among (i) the random-phase approximation, (ii) the Hartree-Fock approximation, and (iii) the approximation originally formulated by Singwi, Tosi, Land, and Sj\"olander. We determine the electron density ${n}_{0}$ and the electron effective mass ${m}^{*}$ so that the results in (iii) accord with the experimental ones. Our calculations give a good description of the energy dispersion and the energy-loss intensity of the 2D PL and the PL decay due to single-particle excitations in the experiment. With an increase in wave number q, the exchange and correlation begin to lower the dispersion curve and make the 2D PL decay at a smaller q value. Our electron system has a high effective density, because it lies on a semi-infinite dielectric medium. However, owing to low dimensionality, the XC effects start to appear remarkably in the 2D PL with an increase in q.

Response dynamics of 1D plasmons coupled to nonlocal bulk plasmons of a host semiconductor

We have carried out an explicit closed-form determination of the inverse dielectric function for a single one-dimensional (1D) quantum wire embedded in a nonlocal 3D bulk semiconductor plasma and analyzed the coupled mode plasmon dispersion relation in the hydrodynamic model. Our analysis shows that the coupled 1D–3D plasmon is damped due to even small nonlocality of the 3D plasma. Also, there is a new nonlocal low frequency mode which does not exist for either the quantum wire or the nonlocal host in the absence of the other.

Crossover from coherent to incoherent excitation of two-dimensional plasmons inGaAs/AlxGa1−xAssingle quantum wells by femtosecond laser pulses

We have investigated the dynamics of two-dimensional (2D) free carrier plasma oscillations in selectively doped $\mathrm{GaAs}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ single quantum wells by time-domain terahertz (THz) emission spectroscopy. Considering both excitation energy and power dependence of the 2D plasmon radiation intensity, we have found two distinct excitation mechanisms of the 2D plasmon; coherent impulsive stimulated Raman process and incoherent sudden heating of the electron system by photoexcited carriers. By monitoring the phase of the emitted THz radiation, a clear crossover from one mechanism to the other is observed as the pump photon energy goes through the absorption edge of the electron system.

Plasmon dispersion in dilute two-dimensional electron systems: Quantum-classical and Wigner crystal–electron liquid crossover

We theoretically calculate the finite-wave-vector plasmon dispersion in a low-density two-dimensional (2D) electron layer taking into account finite temperature, finite layer width, and local-field corrections. We compare our theoretical results with recent Raman-scattering spectroscopic experimental 2D plasmon dispersion data in GaAs quantum wells at very low carrier densities ${(r}_{s}>10)$ and large wave vectors $(q>~{k}_{F}).$ We find good agreement with the experimental data, providing an explanation for why the experimentally measured dispersion seems to obey the simple classical long-wavelength 2D plasmon dispersion formula. We also provide a critical discussion on the observable manifestations of the quantum-classical and the Wigner crystal--electron liquid crossover behavior in the 2D plasmon properties as a function of electron density and temperature in GaAs quantum-well systems.

Two-dimensional plasmon in a surface-state band

By use of electron-energy-loss spectrometer with high-momentum resolution, we have measured a collective electronic excitation in a surface-state band on Si(111)–√3×√3-Ag. We have clarified that the energy dispersion is isotropic with respect to the azimuthal orientation and shows no dependence on the electron probing depth. The obtained energy dispersion agreed very well with the plasmon dispersion calculated from two-dimensional (2D) nearly free-electron theory. As hallmarked from these observations, we identify the measured loss as a longitudinal intraband 2D plasmon in the surface-state band.

Comparison of the collective excitation spectra of three- , two- and one-dimensional electron systems

Collective excitation spectra of three- , two- , and one-dimensional electron systems are deduced theoretically in detail on the basis of random phase approximation in the one subband occupancy limit. The theoretical results show that the plasma energy of the three-dimensional electron gas (3DEG), ω( q), starts from a large value even at q=0, while the plasma energy of the two-dimensional electron gas (2DEG) and one-dimensional (1D) quantum wires start from zero. In contrast to the corresponding plasmon of 3DEG and 2DEG, the dispersion relation of lD plasmon exhibits a logarithmic dispersion at small wave vectors and the characteristic size of the wire appears in the formula. The numerical results show that the wave vector- and energy regions where the 1D plasmons can long exist are much wider than those of 3D and 2D plasmons. This suggests that the collective excitations may play a more important role on the electron transport properties in 1D quantum wires than in 2D and 3D electron systems.

Spin response of 2D electrons to a lateral electric field

The spin orientation of two-dimensional (2D) electrons by a lateral electric field is considered. The electron dispersion law is assumed to contain linear terms due to the spin-orbit band splitting in an asymmetric quantum well. The coefficient of spin orientation in a DC electric field is found. The mean electron spin is oriented in the sample plane perpendicularly to the electric field. The interaction of an AC electric field with spins of 2D electrons is studied. It is shown that transitions between different spin states give rise to a narrow absorption band. These states are mixed with 2D plasmons in the frequency range related to these transitions, with the result being that the plasmon spectrum is modified and a new type of oscillations arises (spin-plasmon polariton). The problem of the generation of spin-plasmon polaritons by an external field is solved.

On the nature of the half-integer quantum features on the transport and Hall resistances of 2D electron systems in a quantizing magnetic field

It is shown that in two-dimensional (2D) electron systems in a quantizing magnetic field, in addition to electron–hole (excitonic) pairing through the Coulomb interaction it is also possible to have Cooper pairing of the 2D electrons due to their interaction with 2D phonons and 2D plasmons localized at the interface of the crystals in semiconductor heterostructures. By summing the divergent (as T→0) ladder diagrams in the zero-sound and Cooper channels, the critical temperatures of the transition to the excitonic and Cooper phases are found. It is shown that the excitonic phase can exist only in comparatively narrow regions near half-integer values of the filling factor ν=(2n−1)/2 (n=1,2,3,…), a finding which is in qualitative agreement with the experimentally observed anisotropic features in the transport resistance of 2D systems in the integer quantum Hall effect regime. By taking into account a superposition of states of bound electron pairs and unpaired 2D electrons in the Cooper phase, one can describe practically all of the experimentally observed quantum features in the fractional quantum Hall effect regime, including at values of ν that are not described by the composite fermion model. At the same time, the interelectron attraction can promote triplet Cooper pairing of composite fermions, which is accompanied by the appearance of an “exotic” quantum feature at ν=5/2. Arguments supporting the possibility of experimental observation of the Cooper phase are presented.

Excitation of 2D plasmons in a Cs/W(110) system

The evolution of surface photoemission spectra was investigated for a Cs/W(110) system with metastable Cs coatings larger than a monolayer. It is demonstrated that 2D plasmons can be detected by threshold photoemission spectroscopy. Three photoemission peaks were observed, whose dependence on the Cs adsorption dose showed a complicated behavior. The peaks may be due to the photoinduced excitation of a plasmon in quasi-2D Cs clusters, a surface Cs plasmon, or an interface Cs-W plasmon.

Coupling of 2D plasmons to nonlocal bulk plasmons

An explicit closed-form position-space expression for the highly inhomogeneous inverse dielectric response function of a quantum well (QW) of finite width (with a single bound subband state) embedded in a bulk medium having a continuum of extended states is derived here analytically. The resulting position-dependent nonlocal dynamic inverse dielectric function ε −1(z,z′; q ||, ω) , given in position representation for the z-direction across the well, depends on the in-plane wave vector q || and frequency ω as well as on the positional variables z, z′. Spatial inhomogeneity arises from the lack of translational invariance in the z-direction due to the presence of the QW. The frequency poles of ε −1(z,z′; q ||, ω) obtained here represent the coupling of nonlocal bulk plasmons with two-dimensional (2D) intrasubband plasmons of the QW. The dispersion relation of the coupled modes is examined. The bulk particle–hole modes damp the collective excitations of the coupled 2D and bulk systems and we estimate the damping rate.

RESONANCE SELECTIVE EXCITATION OF TERAHERTZ PLASMA WAVES IN A SEMICONDUCTOR QUANTUM WELL USING TWO-COLOR LASER RADIATION

A new method of coherent resonance excitation of plasma instability in a 2D quantum well driven by two‐color laser radiation due to photoinduced generation of electron–hole pairs is proposed. It is shown that under the resonance condition, where the frequency and wavenumber of the beat wave obey the 2D plasmon dispersion relation, a space‐charge wave is excited efficiently. A self‐consistent treatment of the problem is presented and the small‐signal response of the 2D system in the THz frequency region is found. This new method provides the selective resonance excitation of plasmons, tuning of their frequency, and efficient control of plasma wave parameters crucial for THz semiconductor technology.

Effect of magnetic field on the coupling of 2D plasmons to nonlocal bulk plasmons

We report here on the effect of a magnetic field on the coupling of 2D plasmons to nonlocal bulk plasmons. The present analysis extends our recent field-free study of the spectrum of coupled collective modes arising from electronic excitations within the quantum well-bound state jointly with those within the continuum of states (but excluding any role of transitions from the bound state to the continuum). We employ a magnetic field generalization of the hydrodynamic model, which correctly represents the magnetic field dependence of the nonlocal principal bulk and 2D plasmons. Our results clearly show how, with increasing magnetic field, some of the modes belonging to the continuum of states split off and have negative dispersion in the long wavelength limit. These are new magnetoplasmons, not to be confused with Bernstein modes (which has been excluded from this analysis).

Dispersive and localized one-dimensional plasmons in very narrow quantum wires

We report on the Raman scattering determination of the dispersion of electronic excitations of 1D electron gases in deep etched GaAs wires, based on high mobility modulation-doped single-quantum wells. From the observation of well-defined 1D plasmons and of uncorrelated electron–hole pair excitations (or spin density waves, depending on the intepretation scheme), we deduce the electron density and lateral confining potential. We demonstrate the fabrication of high-quality 1D systems in the quantum limit, where a single 1D subband is occupied. We quantitatively analyse the measured dispersions and we discuss the possible roles of exchange-correlation corrections and of image charge effects. We critically discuss the interpretation of our results in terms of the Fermi versus Tomonoga–Lüttinger liquid descriptions.

Temperature-Induced Plasmons in a Graphite Sheet

The low-frequency electronic excitations of a two-dimensional graphite sheet are studied within the self-consistent-field approach. A zero-gap graphite sheet only exhibits the interband e-h excitations at zero temperature. Electrons and holes grow rapidly as temperature increases from zero. Temperature induces the intraband excitations and thus the intraband plasmons. A graphite sheet is predicted to be the first undoped system which could exhibit the low-frequency plasmons purely due to temperature. Whether such plasmons exist are mainly determined by temperature and momentum. The temperature-induced plasmons in a graphite sheet are identified as the 2D plasmons from the momentum dependence of plasmon frequencies. They quite differ from the optical plasmons in the three-dimensional graphite or graphite intercalation compounds. The inelastic light scattering spectroscopies could be used to verify the temperature-induced plasmons.

Cooper pairing of two-dimensional electrons in a quantizing magnetic field and the fractional quantum Hall effect

A brief review of the current state of the theory of fractional quantum Hall effect (FQHE) is given along with the assumption of possible connection between the experimentally observed features of the Hall resistance RH of a two-dimensional (2D) electron system in a strong quantizing magnetic field for a fractional filling factor of the lowest Landau level ν=q/(2n+1) with q⩾2, which cannot be described by the Laughlin wave function antisymmetric relative to pair transpositions, and the Cooper pairing of 2D electrons. It is assumed that the electron–electron attraction essential for Cooper pairing can be due to the interaction of 2D electrons with the surface acoustic waves (2D phonons) and the surface 2D plasmons localized near the crystal interfaces (heterojunctions) in the vicinity of inversion layers in the metal–insulator–semiconductor (MIS) structures and heterostructures. The coexistence of coupled electron pairs and unpaired electrons under the FQHE conditions must lead to peculiarities of RH for values of ν described by the Halperin relation following from the symmetry properties of the “mixed” wave function of pairs (bosons) and electrons (fermions). This relation makes it possible in principle to describe all experimental data on FQHE. The summation of “ladder” diagrams diverging according to a power law for T→0 leads to a Bethe–Salpeter-type equation for the vertex part of the electron–electron interaction for a 2D system in a quantizing magnetic field taking into account electron–electron and electron–hole pairing in the Cooper and zero-sound channels. This equation is used to calculate the critical temperature Tc of the phase transition to the state with coupled Cooper pairs and to prove that the value of Tc in the ultra-quantum limit is independent of the effective mass of electrons, i.e., on the 2D density of states. The phase diagram of the 2D system is constructed for the variable electron concentration and magnetic field. It is shown that the region of Cooper pairing of 2D electrons in the case of strong attraction almost coincides with the FQHE region for ν<1, while the region of electron-hole pairing with the formation of charge-density waves (CDW) is expelled to the region with ν>1, which is in accord with the experimental data concerning the CDW-induced features of the longitudinal resistance Rxx for ν=(2n+1)/2 with n⩾2.

Observation of terahertz radiation from higher-order two-dimensional plasmon modes in GaAs/AlGaAs single quantum wells

We have observed terahertz (THz) radiation from higher-order two-dimensional (2D) plasmon modes in GaAs/AlGaAs single quantum wells by time-resolved THz emission spectroscopy. Up to fifth-order plasmon modes are clearly resolved and the observed mode frequencies are in excellent agreement with theory. Relaxation times of the 2D plasmon modes are found to be almost independent of the plasmon wave vector accessible in the present experiment.