Breaking of the overall permutation symmetry in nonlinear optical susceptibilities of one-dimensional periodic dimerized Huckel model

TL;DR

This paper demonstrates analytically that the overall permutation symmetry of nonlinear optical susceptibilities is broken in one-dimensional periodic systems, explaining observed deviations from Kleinman symmetry in such materials.

Contribution

It provides the first analytical proof that the overall permutation symmetry does not hold in periodic systems with delocalized states, unlike molecular systems.

Findings

Permutation symmetry is broken in periodic systems.

Explains deviations from Kleinman symmetry.

Physical conditions for experimental verification.

Abstract

Based on infinite one-dimensional single-electron periodic models of trans-polyacetylene, we show analytically that the overall permutation symmetry of nonlinear optical susceptibilities is, albeit preserved in the molecular systems with only bound states, no longer generally held for the periodic systems. The overall permutation symmetry breakdown provides a fairly natural explanation to the widely observed large deviations of Kleinman symmetry for periodic systems in off-resonant regions. Physical conditions to experimentally test the overall permutation symmetry break are discussed.