Analytical solutions to the third-harmonic generation in trans-polyacetylene: Application of dipole-dipole correlation on the single electron models

TL;DR

This paper derives analytical solutions for third-harmonic generation in trans-polyacetylene models using dipole-dipole correlation, revealing differences from other methods and implications for interpreting experimental peaks.

Contribution

It provides the first analytical solutions for THG in SSH and TLM models using dipole-dipole correlation, highlighting discrepancies with other approaches.

Findings

Van Hove singularity disappears analytically.

Two-photon absorption peak may not be explained by single electron models.

Results differ from static current-current correlation methods.

Abstract

The analytical solutions for the third-harmonic generation (THG) on infinite chains in both Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) models of trans-polyacetylene are obtained through the scheme of dipole-dipole ($DD$) correlation. They are not equivalent to the results obtained through static current-current ($J_0J_0$) correlation or under polarization operator $\hat{P}$. The van Hove singularity disappears exactly in the analytical forms, showing that the experimentally observed two-photon absorption peak (TPA) in THG may not be directly explained by the single electron models.