Correlaction Effects on the Band Gap of Conducting Polymers

TL;DR

This paper investigates how electron correlation effects influence the band gap of conducting polymers, revealing that the nature of interactions (short-range vs long-range) determines whether correlations increase or decrease the band gap.

Contribution

It introduces a projection technique to analyze correlation effects on excitation energies and clarifies the contrasting roles of Hubbard and long-range interactions in band gap modulation.

Findings

Correlation effects can either increase or decrease the band gap depending on interaction type.

Long-range interactions lead to a decrease in band gap due to polarization energy gain.

Screening effects suppress polarization energy, affecting the correlation impact on the band gap.

Abstract

By applying the projection technique to the computation of excitation energies, we study the correlation effects on the band gap of conducting polymers. In the presence of an additional electron or hole, the correlation induces a polarization cloud around the addi- tional particle, which forms a polaron. For the excitation energy of a polaron,there is a competition between a {\it loss} of the correla- tion energy in the ground state and a {\it gain} of polarization energy. For the Hubbard interaction, the {\it loss} of correlation energy is dominant and correlations increase the band gap.However,for long-range interactions, the {\it gain} of polarization energy is dominant and correlations decrease the band gap. Screening the long- range interaction suppresses the {\it gain}of the polarization energy so that correlations again increase the band gap.A small dimerization is always favorable to the correlation effects. For {\it trans}-poly- acetylene, we obtain the on-site repulsion $U=4.4$eV and the nearest- neighbor interaction $V=0.8$ eV. The screening of $\pi$ electrons due to the polarizability of $\sigma$ electrons is quite strong. ** to be published in Phys. Rev. B