Ground-state properties of an electron-phonon coupled quantum wire within the dynamic mean-field approximation

Abstract

Abstract We investigate the ground-state properties of an electron-phonon (e-ph) coupled quantum wire in which the effect of coupling between longitudinal optical (LO) phonons and the wire electrons is considered, in addition to the conventional electron-electron (e-e) interactions. The e-ph coupling is included through the Fröhlich interaction potential and the dynamics of electron correlations using the quantum (dynamic) version of self-consistent mean-field approximation of Singwi et al (the qSTLS approach). Numerical results for static structure factor, pair-correlation function and static density susceptibility are presented over a wide range of electron number density parameter r s . We find that the electrons undergo Wigner crystallization at a critical electron density parameter r s c owing to the dynamics of severely correlated electrons. Notably at a fixed wire width, the inclusion of e-ph coupling tends to increase the value of r s c significantly in comparison to a situation in which only the e-e interactions are considered. Besides this, we compute the plasmon-phonon (pl-ph) coupled modes and the energy contribution of e-ph interactions (E e−ph ) to the ground-state energy of the quantum wire, also known as polaronic energy. We find that pl-ph coupled modes resonantly split into two branches, and ∣E e−ph ∣ monotonically increases with rise in r s then becomes almost constant as r s → r s c . Wherever interesting, we compare our results with the static STLS theory and the lattice regularized diffusion Monte Carlo (LRDMC) simulation data of Casula et al.