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In this paper, we explore the impact of electron-phonon ( e-ph ) coupling on the Wigner crystallization occurring due to strong electron-electron ( e-e ) interactions in a semiconductor-based electron quantum wire. The  e-ph  coupling is represented by the Fröhlich interaction potential and electron correlations are included within the dynamic version of self-consistent mean-field approximation of Hasegawa and Shimizu. Numerical results are reported for the static structure factor and pair-correlation function for fixed wire width and some selected values of electron number density parameter  r s . A strong peak in the static structure factor and pronounced periodic oscillations in pair-correlation function indicate the formation of Wigner crystal in the quantum wire at a critical electron number density  r s c . We find that the inclusion of  e-ph  interactions in addition to the usual  e-e  interactions significantly enhance  r s c , at a fixed wire width.

Impact of electron-phonon interactions on Wigner crystallization in an electron quantum wire