Screw dislocation-induced influence of transverse modes on Hall conductivity

Abstract

The Hall conductivity of an electron gas on an interface showing a topological defect called screw dislocation is investigated. This kind of defect induces a singular torsion on the medium which in turn induces transverse modes in the quantum Hall effect. It is shown that this topology decreases the plateaus’ widths and shifts the steps in the Hall conductivity to lower magnetic fields. The Hall conductivity is neither enhanced nor diminished by the presence of this kind of defect alone. We also consider the presence of two defects on a sample, a screw dislocation together with a disclination. For a specific value of deficit angle, there is a reduction in the Hall conductivity. For an excess of angle, the steps shift to higher magnetic fields and the Hall conductivity is enhanced. Our work could be tested only in common semiconductors but we think it opens a road to the investigation on how topological defects can influence other classes of Hall effect.