SINGLE-PARTICLE QUANTUM STATES IN A CRYSTAL WITH TOPOLOGICAL DEFECTS

The influence of frozen-in topological defects in a crystal on the lon g-wavelength quantum states of a particle is considered. In the contin uum limit of a conveniently defined tight-binding model one is led to a covariant Schrodinger equation on a Riemann-Cartan manifold. When th e tight-binding transfer energies are assumed to depend on the local l attice deformations caused by the defects, additional noncovariant ter ms are generated in the Hamiltonian. These terms generate bound states of the particle to edge dislocations and enhance the scattering of pa rticles on screw dislocations.