Theory of Electron Phenomena in Deformed Crystals

Abstract

On this article there are presented the main results of the theory of electron phenomena in an unordered condensed matter that can be described as an inhomogeneously deformed crystalline lattice with dislocations. The one-electron effective Hamiltonian is derived by introducing a new basis for the expansion of the sought functions. It allows to overcome the difficulty of the discontinuity of the displacement field. The same method is used for the derivation of the equations for eigentones of a deformed crystal, and the equations of the theory of dynamical scattering of electrons by it. The general problem of the description of the totality of electron states in a deformed crystal is discussed, and some new solutions describing localized electron or vibration states are obtained. There is derived and researched the equation of an electrical field generated by the deformation in a crystal with consideration for the interaction of electrons and ions by self-consisted field theory. The tensor kinetic coefficients are obtained, which are proportional to the deformation tensor. Such kind of these coefficients can explain some experimental effects. The appearing of the local superconducting regions and the subsidiary solenoidal current that is generated by a transport one in a deformed superconductor is considered. The behavior and properties of the Abrikosov's vortex in anisotropic and/or deformed superconductors are researched. In more detail this theory has been published in the monograph by the same author of the same title in Russian.