Effects of acoustic-mode localization under dimensional crossover of an electron gas

We have considered the semiconductor heterostructure that localizes acoustic modes within the quantum-well layer. It has been shown that additional confinement of the electrons in the plane of the layer gives rise to a supplementary localization (in a second direction) of acoustic modes. That means, in the many-electron system interacting with the lattice, the crossover from two- to one-dimensional electron-gas behavior leads to the appearance of a collective excitation which consists of lattice vibrations and electron charge-density waves, accompanied by an electrostatic field. The spectrum of this excitation is quite similar to those of acoustic phonons. The excitation is localized in two directions and is one dimensional in character. Splitting of this branch of the excitation from phonon branches of the structure and its additional localization increases with the wave vector of the excitation q. The two-dimensional electron gas forming a conductive channel with submicrometer dimensions completely localizes the excitation within this channel. If the electron gas is confined further to a one-dimensional channel, the excitation reveals maxima in the splitting and localization in the region q≈(Formula presented), (Formula presented) being the Fermi wave vector. In this region the dispersion curve of the excitation shows rotonlike behavior and the density of states has a peak (T=0).