Disclinations in the geometric theory of defects

Abstract

In the geometric theory of defects, media with a spin structure, for example, ferromagnet, is considered as a manifold with given Riemann--Cartan geometry. We consider the case with the Euclidean metric corresponding to the absence of elastic deformations but with nontrivial $\mathbb{S}\mathbb{O}(3)$-connection which produces nontrivial curvature and torsion tensors. We show that the 't Hooft--Polyakov monopole has physical interpretation in solid state physics describing media with continuous distribution of dislocations and disclinations. The Chern--Simons action is used for the description of single disclinations. Two examples of point disclinations are considered: spherically symmetric point "hedgehog" disclination and the point disclination for which the $n$-field has a fixed value at infinity and essential singularity at the origin. The example of linear disclinations with the Franc vector divisible by $2\pi$ is considered.

21 pages, 6 figures

References in corpus (5)

• Geometric Phases in Graphitic Cones
• The 't Hooft-Polyakov monopole in the geometric theory of defects
• Inside the BTZ black hole
• Torsional Elastic Waves in Double Wall Tube
• Gauge parameterization of the $n$-field

Cited by in corpus (3)

• On Nanocones as a Gravitational Analog System
• Spherically symmetric 't Hooft-Polyakov monopoles
• Reformulation of continuum defects in terms of the general teleparallel geometry in the language of exterior algebra