The Topological Origin of the Peierls-Nabarro Barrier

TL;DR

This paper reveals that the topological structure of ground state manifolds in density wave systems causes dislocations to split into disclinations, which constrains their movement and creates an energy barrier known as the Peierls-Nabarro barrier.

Contribution

It introduces a topological explanation for the Peierls-Nabarro barrier based on the splitting of dislocations into disclinations within the ground state manifold.

Findings

Dislocations split into disclinations due to topology.

Disclinations are confined to specific points in the GSM.

Topology prevents zero-energy dislocation glide.

Abstract

Crystals and other condensed matter systems described by density waves often exhibit dislocations. Here we show, by considering the topology of the ground state manifolds (GSMs) of such systems, that dislocations in the density phase field always split into disclinations, and that the disclinations themselves are constrained to sit at particular points in the GSM. Consequently, the topology of the GSM forbids zero-energy dislocation glide, giving rise to a Peirels-Nabarro barrier.