Renormalization of acoustic phonon spectra and rudiments of the Peierls transition in free-standing quantum wires

We have analyzed a quasi-one-dimensional electron-phonon system coupled thr ough the deformation potential interaction. In a free-standing quantum wire , we calculated the renormalization of acoustic phonon spectra. The results illustrate remarkable cusplike features in the vicinity of the phonon wave vector that is twice the electron Fermi wave vector. These cusps are rudim ents of the Peierls transition in the quasi-one-dimensional system. The tra nsition is suppressed in conventional materials because of the electrostati c effects. For such materials, however, the renormalization of acoustic pho non spectra and the cusps can be observed in various acoustical and optical experiments. Furthermore, our study demonstrates that the Peierls transiti on can occur in free-standing quantum wires fabricated from semiconductor m aterials with high permittivity. [S0163-1829(98)05638-3].