Phase instability and electron-assisted renormalization of acoustic phononspectrum in free-standing quantum wires

In this paper we consider the possibility of a Peierls phase transition for a system of one-dimensional electrons and acoustic phonons confined in a f ree-standing quantum wire (FSQWI). We assume that electrons and phonons are coupled via the deformation potential interaction. The dispersion relation for this system is derived taking into account the role of electrostatic e ffects. The Peierls phase transition to the state characterized by periodic lattice deformation (PLD) is obtained in the high-permittivity limit. The formalism developed in this paper facilitates investigation of the renormal ized acoustic phonon spectrum and predicts the possibility of the Peierls t ransition in FSQWIs fabricated from semiconductor materials with large perm ittivity. (C) 1999 Elsevier Science B.V. All rights reserved.