On the intrinsic pinning and shape of charge-density waves in 1D Peierls systems

TL;DR

This paper investigates how nonlinear effects influence charge-density waves in 1D Peierls systems, revealing that non-integrability leads to wave pinning and formation of localized electron bonds, contrasting with the idealized cosine wave assumption.

Contribution

It provides an exact analytical solution for a nonlinear charge-density wave model and demonstrates how non-integrability causes wave pinning and bond localization in Peierls systems.

Findings

Exact cnoidal wave solution at integrable points

Non-integrability induces wave pinning and bond formation

Aubry transition from sliding to pinned phase

Abstract

Within the standard perturbative approach of Peierls, a charge-density wave is usually assumed to have a cosine shape of weak amplitude. In nonlinear physics, we know that waves can be deformed. What are the effects of the nonlinearities of the electron-lattice models in the physical properties of Peierls systems? We study in details a nonlinear discrete model, introduced by Brazovskii, Dzyaloshinskii and Krichever. First, we recall its exact analytical solution at integrable points. It is a cnoidal wave, with a continuous envelope, which may slide over the lattice potential at no energy cost, following Fr\"ohlich's argument. Second, we show numerically that integrability-breaking terms modify some important physical properties. The envelope function may become discontinuous: electrons form stronger chemical bonds which are local dimers or oligomers. We show that an Aubry transition from the sliding phase to an insulating pinned phase occurs when the model is no longer integrable.