Electron Pairing and Coulomb Repulsion in One-Dimensional Anharmonic Lattices

TL;DR

This paper demonstrates that in one-dimensional anharmonic lattices, electron pairing into localized bisolectron states is possible due to lattice deformation overcoming Coulomb repulsion, with analytical and numerical methods showing qualitative agreement.

Contribution

It introduces a new analytical and numerical analysis of electron pairing in anharmonic lattices, including the effects of Coulomb repulsion and lattice deformation.

Findings

Localized bisolectron states can form in anharmonic lattices.

Analytical and numerical results agree qualitatively over broad parameters.

Critical Coulomb repulsion values for unbinding are estimated.

Abstract

We show that in anharmonic one-dimensional crystal lattices pairing of electrons or holes in a localized bisolectron state is possible due to coupling between the charges and the lattice deformation that can overcompensate the Coulomb repulsion. Such localized soliton-like states appear as traveling ground bound singlet states of two extra electrons in the potential well created by the local lattice deformation. We also find the first excited localized state of two electrons in a soliton-like lattice deformation potential well given by a triplet state of two electrons. The results of the analytical study of interacting electrons in a lattice with cubic anharmonicity are compared with the numerical simulations of two electrons in an anharmonic lattice taking into account of the (local) Hubbard electron-electron repulsion. We qualitative agreement between both approaches for a broad interval of parameter values. For illustration we give expressions for the bisolectron binding energy with parameter values that are typical for biological macromolecules. We estimate critical values of Coulomb repulsion where the bisolectron becomes unbound.