ANOMALOUS DEFECTS AND THEIR QUANTIZED TRANSVERSE CONDUCTIVITIES

Using a description of defects in solids in terms of three-dimensional gravity, we study the propagation of electrons in the background of d isclinations and screw dislocations. We study the situations where the re are bound states that are effectively localized on the defect and h ence can be described in terms of an effective (1 + 1)-dimensional fie ld theory for the low energy excitations. In the case of screw disloca tions, we find that these excitations are chiral and can be described by an effective field theory of chiral fermions. Fermions of both chir ality occur even for a given direction of the magnetic field. The ''ne t'' chirality of the system however is not always the same for a given direction of the magnetic held, but changes from one sign of the chir ality through zero to the other sign as the Fermi momentum or the magn itude of the magnetic flux is varied. On coupling to an external elect romagnetic field, the latter becomes anomalous and predicts novel cond uction properties for these materials.