Short-wavelength plasmons in low-dimensional systems
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C PROPERTIES OF SOLIDS
Short-Wavelength Plasmons in Low-Dimensional Systems R. Z. Vitlina, L. I. Magarill*, and A. V. Chaplik Institute of Semiconductor Physics, Russian Academy of Sciences, Siberian Branch, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia *e-mail: [email protected] Received July 6, 2007
Abstract—The dispersion of plasma waves in systems of various dimensions is investigated up to the end point of the spectrum. In 2D and 3D systems, the plasmon spectrum still ends (due to Landau damping) within the applicability range of the quasi-classical approximation, i.e., for k pF (k is the plasmon momentum and pF is the electron Fermi momentum). In 1D systems, the results are qualitatively different, since the Landau damping is concentrated in a region where the quantum effects cannot be ignored. This peculiarity of 1D systems gives rise to undamped branches of acoustic plasmons with a phase velocity lower than the electron Fermi velocity in multicomponent 1D plasmas. PACS numbers: 72.15.Nj, 73.20.Mf, 73.22.Lp DOI: 10.1134/S1063776108040195
1. INTRODUCTION Recent years have been marked by a revived interest in plasma waves in low-dimensional systems and nanostructures. This is attributable to significant progress in the technology of producing perfect structures, to advances in the technique of exciting and recording such oscillations, and to the possibilities of their practical applications in terahertz electromagnetic wave engineering. The currently available experiments with lowdimensional plasmons pertain to the long-wavelength limit: the plasmon momenta k are much smaller than the electron Fermi momentum pF . In this case, the spatial dispersion in the dynamic conductivity may be ignored and the electron system may be considered as a continuum. The same condition k pF is a criterion for a quasi-classical consideration of the problem. In addition, plasma waves undergo no Landau damping 0 and at zero temperature. for k/pF Since the nanometer scales have become quite accessible for modern lithography and the electron Fermi wavelength in typical 2D systems is ~10–30 nm, the question of how the dispersion curves of 1D and 2D plasmons behave in the short-wavelength region up to the end point of the plasmon spectrum seems quite topical. This point is determined by the boundary of the single-particle excitation continuum (electron–hole continuum; we have in mind a hole beneath the Fermi surface), since it is in this place that the Landau damping “switches on”. As we will show below, the plasmon dispersion law ω(k) found in the random-phase approximation (RPA) determines the end point of the spectrum k0 in 2D and 3D systems that lies at k0 pF in the “metallic” limit of a dense plasma, pFaB/ 1 (aB is the
effective Bohr radius). The 1D case (a quantum wire, a nanotube) is special in several respects. First, the dispersion law ω(k) formally found in the RPA has no end point at all. Second, in the 1D case, the Landau damping region is bounded on the frequency axis both above and below, while t
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