Electronic oscillations in paired polyacetylene chains

TL;DR

This paper models paired polyacetylene chains using a quantum field approach, revealing energy gaps and oscillation phenomena linked to soliton formation and symmetry breaking.

Contribution

It introduces a novel theoretical framework combining tight-binding and Dirac models to analyze electronic oscillations in coupled polyacetylene chains.

Findings

Energy gap due to mass-matrix in Dirac Lagrangian

Soliton formation via spontaneous symmetry breaking

Particle oscillations analogous to Bloch oscillations

Abstract

An interacting pair of polyacetylene chains are initially modeled as a couple of undimerized polymers described by a Hamiltonian based on the tight-binding model representing the electronic behavior along the linear chain, plus a Dirac's potential double well representing the interaction between the chains. A theoretical field formalism is employed, and we find that the system exhibits a gap in its energy band due to the presence of a mass-matrix term in the Dirac's Lagrangian that describes the system. The Peierls instability is introduced in the chains by coupling a scalar field to the fermions of the theory via spontaneous symmetry breaking, to obtain a kink-like soliton, which separates two vacuum regions, i.e., two spacial configurations (enantiomers) of the each molecule. Since that mass-matrix and the pseudo-spin operator do not commute in the same quantum representation, we demonstrate that there is a particle oscillation phenomenon with a periodicity equivalent to the Bloch oscillations.