Polaron and bipolaron formation in a cubic perovskite lattice

TL;DR

This paper investigates polaron and bipolaron formation in a three-dimensional oxide lattice using exact diagonalization, revealing strong localization effects and the influence of Coulomb interactions on their stability.

Contribution

It provides a detailed numerical analysis of polaron and bipolaron stability in a cubic perovskite lattice, including vibrational excitations and Coulomb effects, with comparisons to variational methods.

Findings

Polarons are highly localized with a single vibrational state.

Bipolaron formation is suppressed at realistic Coulomb repulsions.

A large parameter window exists where polarons are stable but bipolarons are not.

Abstract

The Rice-Sneddon model for BaBiO$_3$ is a nice model Hamiltonian for considering the properties of polarons and bipolarons in a three-dimensional oxide crystal. We use exact diagonalization methods on finite samples to study the stability and properties of polarons and bipolarons. Because polarons, when they form, turn out to be very well-localized, we are able to converge accurately our calculations for two-electron bipolaron wavefunctions, accounting for the Coulomb interaction without approximation. Some of our results are compared with and interpreted by reference to the variational method of Landau and Pekar. We calculate both electronic and vibrational excitations of the small polaron solutions, finding a single vibrational state localized with the full symmetry of the polaron, which has its energy significantly increased. Both on-site (Hubbard) and long-range Coulomb repulsion are included in the bipolaron calculation, but due to the high degree of localization, the long-range part has only a small influence. For a reasonable on-site repulsion $U$ equal to 2 times the band width $W$, bipolaron formation is significantly suppressed; there is a large window of electron-phonon coupling where the polaron is stable but the bipolaron decays into two polarons.