Hall conductivity in the cosmic defect and dislocation space-time

TL;DR

This paper explores how topological defects and dislocations in spacetime affect charge conductivity and the quantum Hall effect, revealing that spacetime deformations induce currents and modify Hall conductivity.

Contribution

It introduces a novel analysis of how cosmic defects influence quantum Hall effects and conductivity in curved spacetime, providing new insights into topological spacetime effects.

Findings

Spacetime defects induce electric currents at leading order.

Deformations alter the Hall conductivity based on external fields and sample size.

Corrections depend on particle momentum and spacetime topology.

Abstract

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.