A general expression was derived for the k•p Hamiltonian in crystals with linear topological defects such as dislocations, disclinations, and dispirations. It was shown to include gauge potential terms which corresponded to a non-Abelian gauge group, E(3), which was the proper Euclidean group. The gauge field was confined within the cores of topological defects, and influenced carriers in the bulk of the crystal via the gauge potential which extended beyond it. A general expression for the latter potential was presented. In the case of a crystal which contained only dislocations, the gauge group E(3) degenerated into T(3); the Abelian sub-group of translations.

Gauge Properties of Hamiltonians for Crystals with Linear Topological Defects. Y.T.Rebane: Physical Review B, 1995, 52[3], 1590-5