Classical continuum theory of the dipole-forbidden collective excitations in quantum strips.

We investigate the collective mode excitation spectrum of an electron gas in a quantum strip that is subjected to a perpendicular magnetic field, with emphasis on the dipole-forbidden transitions. The quantum strip is assumed to be defined in a two-dimensional electron gas by the application of a parabolic confining potential. A classical continuum theory of the collective modes is developed and solved exactly. These results are used to determine the density-response functions. An experimental method to detect the dipole-forbidden modes, based on the use of an asymmetric planar metal grating above an array of quantum strips, is proposed, and calculations of the expected infrared transmission spectrum of the combined grating-strip system are presented. In a system with reasonable parameters, we find that some of the dipole-forbidden absorption peaks are large enough to be observable.