# The driving force behind the distortion of one-dimensional monatomic chains - Peierls theorem revisited

## TL;DR

This paper revisits Peierls theorem for one-dimensional monatomic chains, revealing that electrostatic interactions, not band gap formation, primarily drive distortion, which depends on external conditions and force balances.

## Contribution

It demonstrates that chain distortion is conditional and driven mainly by electrostatic forces, challenging the traditional view that band gap formation is the primary cause.

## Key findings

- Electrostatic interactions are the main driving force for distortion.
- Distortion depends on the balance of forces and external conditions.
- The electronic kinetic energy stabilizes the symmetric configuration.

## Abstract

The onset of distortion in one-dimensional monatomic chains with partially filled valence bands is considered to be well-established by the Peierls theorem, which associates the distortion with the formation of a band gap and a subsequent gain in energy. Employing modern total energy methods on the test cases of lithium, sodium and carbon chains, we reveal that the distortion is not universal, but conditional upon the balance between distorting and stabilizing forces. Furthermore, in all systems studied, the electrostatic interactions between the electrons and ions act as the main driving force for distortion, rather than the electron band lowering at the Fermi level as is commonly believed. The main stabilizing force which drives the chains toward their symmetric arrangement is derived from the electronic kinetic energy. Both forces are affected by the external conditions, e.g. stress, and consequently the instability of one-dimensional nanowires is conditional upon them. This brings a new perspective to the field of one-dimensional metals, and may shed new light on the distortion of more complex structures.