A general expression for the k⋅p Hamiltonian in crystals with linear topological defects such as dislocations, disclinations, and dispirations has been found. It has been shown to contain gauge potential terms corresponding to a non-Abelian gauge group, E(3), which is the proper Euclidean group. The gauge field is confined within the cores of topological defects and influences the carriers in the bulk of the crystal through the gauge potential which extends beyond it. A general expression for the gauge potential A(r) is presented. For a crystal that contains only dislocations the gauge group E(3) degenerates into T(3), the Abelian subgroup of translations. The corresponding gauge potential becomes A^(r)=i${\mathrm{\beta }}^{\mathit{T}}$(r)(p^/ħ-${\mathbf{k}}_{\mathrm{\alpha }}$), where ${\mathbf{k}}_{\mathrm{\alpha }}$ is the electron wave vector related to the point in the Brillouin zone for which the k⋅p Hamiltonian is written, p^ is the momentum-operator matrix in the basis of Bloch functions corresponding to ${\mathbf{k}}_{\mathrm{\alpha }}$, and β(r) is the distortion tensor.

• Received 15 March 1995

DOI:https://doi.org/10.1103/PhysRevB.52.1590