Universal Curvature Force on Dislocations from a Cartan Geometric Defect Action

TL;DR

This paper introduces a unified geometric framework linking dislocations, disclinations, and phase defects in materials, predicting a universal curvature-induced force on dislocations and phenomena observable in experiments.

Contribution

It develops a Cartan geometric theory that unifies defect types and predicts a universal force on dislocations from curvature, with testable experimental implications.

Findings

Universal Magnus-like force on dislocations due to curvature

Disclination-driven reconnection events

Testable signatures in colloidal crystals and metamaterials

Abstract

We develop a unified Cartan geometric framework where dislocations and disclinations correspond to torsion and curvature of the material coframe connection, respectively, and phase defects emerge as U(1) vortices. This single action principle produces coupled equations of motion and conservation laws governing these defects. Our theory predicts a universal Magnus-like force exerted by curvature on moving dislocations, as well as disclination-driven reconnection events. These phenomena offer experimentally testable signatures in colloidal crystals and mechanical metamaterials.