The spectrum of the collective excitations of a magnetoplasma, confined in a quasi-one-dimensional quantum-well wire is analyzed. The dispersion relations of the intrasubband and intersubband magnetoplasmons are calculated with excellent agreement to experimental results. The calculations are done in the random-phase approximation with no further simplifying approximation. We find analytical results for the dispersion relations of the intrasubband and intersubband magnetoplasmons.The spectrum of the collective excitations of a quasione-dimensional electron gas (Q1DEG) in the absence' and in the presence of a quantizing magnetic field ' has been explored theoretically' and experimentally. ' Some fundamental questions about the many-particle behavior of the Q1DEG remain open up to now. One of these is the question of whether the Q1DEG is better described as a Fermi liquid, or if the model of a Tomonaga-Luttinger liquid is more appropriate. In fact, the strictly 1D Fermi system is a singular, strongly correlated manybody system where any interaction between the electrons leads to essential singularities. But on the other hand, experimental results' ' and theoretical investigations'show that the Q1DEG is quantitatively well described by the random-phase approximation (RPA}, i.e. , in the lowest order of the Feynman-Dyson perturbation series of a Q1D Fermi liquid. Also in the case where exchange-correlation eS'ects, ignored in the RPA, become important the Fermi-liquid model treated within the time-dependent Hartree-Fock approximation is appropriate to describe the resulting effects.In this paper, we present a quantum theory of Q1D magnetoplasmons in quantum-well wires (QWW) within the RPA, without further approximations on the RPA.Hence, our theory is valid for all wave vectors, magnetic-field strengths, and electron densities as long as the RPA is valid. We study the single QWW by a model in which the electrons are confined in a zero-thickness I x-y plane along the z direction at z =0. In the y direction the electron motion is quantum-confined by an efFective potential, assumed to be parabolic: V,s(y)=mQ y /2.Choosing the Landau gauge A=( -y8, 0, 0) for the vector potential of the external applied magnetic field B=(O,O, B) and ignoring the Zeeman spin splitting, the single-particle Hamiltonian is exactly solvable with the single-particle wave function (x~N, k")=%zk (x)=1/QL"e " 4N(y -Yk )y(z), where 4N(y -Yk } is the shifted harmonic-oscillator x wave function. The corresponding energy eigenvalues are 8 (Nk")=A' co(N+ -, ')+R k"/2m; N=0, 1,2, . . . . In these equations the center coordinate is Yk =@Peak", where T~=(fi/mco, )'~i s the typical width of the wave function and y =to, /to, . Further, co, =(co2+0 )'~i s the hybrid frequency, co, =e8/m is the cyclotron frequency, and m =m(to, /0) is the renormalized magnetic-fielddependent mass.The single-particle Hamiltonian of the electrons of the Q1DEG in the presence of an external perturbation is written as H=HO+H& where Ho is the unperturbed Hamiltonian and H& = V"(x,...
We present an investigation of the plasmon excitations in a quasi-one-dimensional metal, the blue bronze K 0.3 MoO 3 . The dispersion relation along the one-dimensional direction, as measured by electron energy-loss spectroscopy in transmission, is quasilinear over a wide momentum range before it exhibits a negative curvature. We show that the quasilinear part can be explained within an essentially three-dimensional model based on the random-phase approximation. Band-structure effects are thereby considered through the Ehrenreich-Cohen formula, tailor-made to the specific, strongly anisotropic material. From this analysis, we find no hint for exceptional properties caused by one dimensionality as is currently discussed in the context of photoemission measurements. The genuine dependence of the plasmon modes on the propagation angle relative to the one-dimensional axis is masked by interband transitions lying at about the same energy as the plasmon excitations itself.
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