Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons

TL;DR

This paper investigates how electron-phonon interactions influence correlation behaviors in one-dimensional electron systems, revealing shared correlation patterns and the conditions under which these correlations become long-ranged.

Contribution

It demonstrates the shared correlation of electron density and phonon displacement fields and characterizes their range depending on system dimensionality and electron interactions.

Findings

Shared $2k_F$-wave correlations between electrons and phonons.

Quasi-long-ranged correlations in single chains with 1D or 3D phonons.

Long-ranged correlations in 3D arrays with repulsive interactions.

Abstract

Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2k_F$-wave components of the electron density and phonon displacement field share the same correlations. Both correlations are quasi-long-ranged for a single conducting chain coupled to one-dimensional or three-dimensional phonons, and they are long-ranged for repulsive electron-electron interactions for a three-dimensional array of parallel one-dimensional conducting chains coupled to three-dimensional phonons.