The Scattering of Tight-Binding Electrons Due to the Long-Ranged Topological Disorder Off a Screw Dislocation in Semiconductors

The tight-binding equation for electrons in a semiconductor of a perfect lattice is separated by a unitary matrix into equations, each of which corresponds to the Scrödinger equation to an electron belonging to an energy band. The same separation is possible as for the tight-binding electrons in the screw dislocation if the tight-binding parameters are assumed constant: no interband transition occur in this model. Although the mass tensor is anisotropic, the problem is equivalent to the Aharonov-Bohm problem, whose scattering theoretical solution was obtained already.