  Influences of topological defect and dislocation on conductivity behavior of
charge carries in external electromagnetic fields are studied. Particularly the
quantum Hall effect is investigated in detail. It is found that the nontrivial
deformations of spacetime due to topological defect and dislocation produce an
electric current at the leading order of perturbation theory. This current then
induces a deformation on the Hall conductivity. The corrections on the Hall
conductivity depend on the external electric fields, the size of the sample and
the momentum of the particle.

Mesoscale and Nanoscale Physics;High Energy Physics - Theory