  The existence and nature of a new mode of electronic collective excitations
(quadrupole plasmons) in confined one-dimensional electronic systems have been
predicted by an eigen-equation method. The eigen-equation based on the
time-dependent density-functional theory is presented for calculating the
collective excitations in confined systems. With this method, all modes of
collective excitations in the 1D systems may be found out. These modes include
dipole plasmons and quadrupole plasmons. The dipole plasmon mode corresponds to
the antisymmetric oscillation of induced charge, and can be shown as a
resonance of the dipole response. In the quadrupole plasmon modes, the induced
charge distribution is symmetric, and the dipole response vanishes. The motion
of the electrons in the quadrupole modes is similar to the vibration of atoms
in the breathing mode of phonons. This type of plasmons can be shown as a
resonance of the quadrupole response, and has to be excited by al non-uniform
field.

Mesoscale and Nanoscale Physics