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

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We have analyzed a quasi-one-dimensional electron-phonon system coupled through 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 rudiments of the Peierls transition in the quasi-one-dimensional system. The transition is suppressed in conventional materials because of the electrostatic effects. For such materials, however, the renormalization of acoustic phonon spectra and the cusps can be observed in various acoustical and optical experiments. Furthermore, our study demonstrates that the Peierls transition can occur in free-standing quantum wires fabricated from semiconductor materials with high permittivity.