ELECTRON-ELECTRON INTERACTIONS IN QUASI-ONE-DIMENSIONAL ELECTRON-SYSTEMS

We present an analytical calculation for the Coulomb matrix elements in a quasi-one-dimensional system using a harmonic-confinement-potential model. We show that the intrasubband Coulomb interaction keeps the typical logarithmic divergent behavior of the strictly one-dimensional system in the long-wavelength limit, while the intersubband Coulomb interaction approaches discrete values depending on the relevant subbands. In applying our analytical form of the Coulomb matrix to study the intersubband collective excitations with a single-subband separation in the long-wavelength limit, we obtain analytical expressions for the intersubband plasmon frequencies and find that there are M different modes composing the collective excitations of a system with M populated subbands. The physical origin of these M modes is due to the different Fermi momenta of the electrons in different subbands. The maximum value of the intersubband plasmon frequency estimated by our theory is in good agreement with the existing experimental data. © 1990 The American Physical Society.