Polaron and bipolaron dispersion curves in one dimension for intermediate coupling

TL;DR

This paper calculates bipolaron dispersion curves in one dimension at intermediate coupling using a variational method, comparing results with other models and analyzing effective masses.

Contribution

It introduces a variational approach for bipolaron energies at intermediate coupling in a model with specific electron-phonon interactions and Coulomb repulsion.

Findings

Bipolaron energies as a function of wave vector are calculated.

Effective masses at the zone center are obtained.

Comparison with Hubbard-Holstein model data shows differences in band structure effects.

Abstract

Bipolaron energies are calculated as a function of wave vector by a variational method of Gurari appropriate for weak or intermediate coupling strengths, for a model with electron-phonon interactions independent of phonon wave vectors and a short-ranged Coulomb repulsion. It is assumed that the bare electrons have a constant effective mass. A two-parameter trial function is taken for the relative motion of the two electrons in the bipolaron. Energies of bipolarons are compared with those of two single polarons as a function of wave vector for various parameter values. Results for effective masses at the zone center are also obtained. Comparison is made with data of other authors for bipolarons in the Hubbard-Holstein model, which differs mainly from the present model in that it has a tight-binding band structure for the bare electrons.