Electrostatically-induced topological phase transitions in polyacetylene molecules

TL;DR

This study investigates how external gate voltages induce topological phase transitions in polyacetylene molecules, revealing the role of Coulomb interactions and topological invariants in electronic and lattice properties.

Contribution

The paper introduces a continuum model using Abelian bosonization to analyze electrostatically induced topological phases in polyacetylene, incorporating electron-electron interactions and topological invariants.

Findings

Gate voltage induces topological phase transitions in polyacetylene.

Coulomb interactions modify the topological phase diagram.

Topological sectors are characterized by an integer invariant q.

Abstract

We study the electronic properties of a linear trans-polyacetylene (tPA) molecule capacitively coupled to an external gate voltage $V_g$ of width $d$. We describe this system using the Takayama-Lin-Liu-Maki (TLM) model in the continuum, and analyze it within the Abelian bosonization formalism, which allows us to treat both electronic and lattice degrees of freedom and to incorporate the effects of repulsive Coulomb interactions among electrons. The global ground state describing simultaneously the electronic charge-density field as well as the lattice dimerization field of a tPA molecule is shown to consist of multikink solutions of a modified sine-Gordon equation for the charge-density field, which is controlled by $V_g$, the width $d$, and the Luttinger parameter $K$ encoding the strength of electron-electron interactions. These solutions belong to distinct topological sectors labeled by an integer invariant $q$ that simultaneously quantifies both the bound charge and the number of domain walls in the dimerization pattern induced at the gated region. Increasing $V_g$ drives a sequence of topological phase transitions characterized by abrupt changes in $q$. We further examine the effect of repulsive Coulomb interactions on the resulting topological phase diagram, and finally, we discuss the relevance of our findings for potential nanoelectronic devices based on gated tPA molecules.