ar X iv : c on d - m at / 0 11 21 92 v 1 1 1 D ec 2 00 1 1 Theory of Electron Phenomena in Deformed Crystals

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 in-homogeneously 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 eigentone 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 the 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 super-conductors are researched. In more detail this theory has been published in the monograph by the same author of the same title in Russian. In the title of this article as the " deformed crystal " the unordered solid-state substance is named. In this crystal the equilibrium sites of atoms form a lattice that can be described as a inhomogeneously deformed crystalline lattice with dislocations. The electron potential energy differs from the periodic function of coordinates in other way than in a crystal disordered by localized defects, e. g., interstitial or substitutional impurities. In the site representation these cases can be considered as alternative limiting cases, because the localized defects are described by the diagonal disorder, but a deformation changes the non-diagonal hamiltonian elements and makes them dependent on site coordinates, and not only on their differences. Electron phenomena in non-ideal crystals with localized defects have been investigated in a very large number of experimental and theoretical works. Deformed crystals have been investigated poorly, and 1