The bipolaron in the strong coupling limit

TL;DR

This paper investigates bipolaron formation in ionic crystals within the strong coupling limit, establishing conditions for bound states and validating the Pekar-Tomasevich energy functional.

Contribution

It proves the validity of the Pekar-Tomasevich functional in the strong coupling limit and provides conditions for bipolaron binding and ground state existence.

Findings

Bound bipolaron states exist under certain coupling conditions.

The Pekar-Tomasevich energy functional accurately describes the system in the strong coupling limit.

Ground states exist for total momentum below a certain threshold.

Abstract

The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Fr\"{o}hlich approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons. Otherwise the electrons form a bound pair. We prove the validity of the Pekar-Tomasevich energy functional in the strong coupling limit, yielding estimates on the coupling parameters for which the binding energy is strictly positive. Under the condition of a strictly positive binding energy we prove the existence of a ground state at fixed total momentum $P$, provided $P$ is not too large.