| Research Abstract |
1.It is pointed out that 2-dimensional electrons located at the interface of semiconductor hetero-structures such as Si-MOS experience the localized-delocalized transition by the influence of impurities in oxides. We have shown by using the path-integral formalism that when electrons form an electron crystal or Wigner lattice, the Wigner phonon spectra have an energy gap in the long wave-length limit, and that the electrons are localized. The line-shape of the micro-wave absorption is not of the Lorentzian type but asymmetric owing to the density of states of the Wigner phonons.
2.Kono et al. measured the plasmon resonance of quasi-2-dimensional electrons on liquid helium 3 at very low temperatures and found that (a) the resonance position is almost independent of temperature, and (b) the line-width is roughly proportional to temperature. By assuming that the 2-dimensional electrons form a Wigner crystal which interacts with the surface capillary waves or ripplons of liquid helium, we have calculated the line-width of the plasmon resonance by the linear ac conductivity formula obtained by the path-integral method. The results show that the line-width is proportional to temperature and is in good agreement with experiments. This temperature dependence comes from the number of scatterers, i. e., of thermally excited ripplons.
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