Quantum motion of electrons in topologically distorted crystals

For the description of the long-wavelength quantum states of electrons in c rystals with topological defects we establish a general framework on the ba sis of the continuum theory of defects. The resulting one-particle Schrodin ger equation lives on a Riemann-Cartan manifold, representing the distorted crystal, and consists of two parts. All effects due to the topology of the defects are contained in the first part which has a covariant form and des cribes the purely geometric particle motion. The second part is non-covaria nt and derives from de formation-dependent funneling rates of the particle which e.g. are responsible for the existence of bound states to edge disloc ations.