Effect of the Image Potential on Plasmons in Cylindrical Quantum-Well Wires

The collective electronic excitations in quasi‐one‐dimensional cylindrical quantum‐well wires are studied theoretically. Using a two‐subband model the dispersion curves of the intra‐ and intersubband plasmons in the random‐phase approximation for the cases of one and two occupied subbands are calculated. The influence of the image forces on the intra‐ and intersubband plasmon is studied in detail. New explicit analytical expressions for the dispersion relations, valid in a wide range of the wave vector are derived. It is shown that the additional intrasubband plasmon, arising if two subbands are occupied, has for small wave vectors a linear dispersion and is independent of the dielectric screening of the quantum‐well wire. The intersubband plasmon is split in two branches, one with a positive and one with a negative dispersion. The electric dipole moment of the collective excitations is calculated and the selection rules for the coupling of light with the plasmons are derived.