Effects of the Lattice Discreteness on a Soliton in the Su-Schrieffer-Heeger Model

TL;DR

This study analytically examines how lattice discreteness influences electron band structures in the SSH model, revealing localized states near band edges induced by solitons, and introduces a modified TLM model consistent with numerical results.

Contribution

A modified TLM model derived from the SSH model is proposed to analytically describe weakly localized states caused by lattice discreteness.

Findings

Localized states are attracted to solitons at band edges.

Analytical solutions match numerical simulations.

Band structure remains unchanged by the soliton presence.

Abstract

In this paper we analytically study the effects of the lattice discreteness on the electron band in the SSH model. We propose a modified version of the TLM model which is derived from the SSH model using a continuum approximation. When a soliton is induced in the electron-lattice system, the electron scattering states both at the bottom of the valence band and the top of the conduction band are attracted to the soliton. This attractive force induces weakly localized electronic states at the band edges. Using the modified version of the TLM model, we have succeeded in obtaining analytical solutions of the weakly localized states and the extended states near the bottom of the valence band and the top of the conduction band. This band structure does not modify the order parameters. Our result coincides well with numerical simulation works.