Hall Conductivity in the Cosmic Defect and Dislocation Spacetime

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.

Topological and rotating effects on the Dirac field in the spiral dislocation spacetime

“…where φ = φ (r, ϕ, z) and ξ = ξ (r, ϕ, z) are two-spinors. By substituting ( 16) into the Dirac equation (15), we obtain two coupled equations of φ and χ. The first coupled equation is…”

Harmonic oscillator in an elastic medium with a spiral dislocation

“…The common point between these areas of physics is the description of these defects made by the Volterra process [1,2,4,5]. Up to now, a great deal of study has explored quantum system in the presence of disclinations [6][7][8][9][10] and screw dislocations [5,[11][12][13][14][15][16] in the context of condensed matter physics. In particular, torsion effects related to the presence of topological defects are in the interests of studies of semiconductors [17][18][19][20].…”

On an atom with a magnetic quadrupole moment in a rotating frame

“…Hall effect [73], quantum scattering [74][75][76], spin currents [77], cylindrical shells [78] and geometric quantum phases [79,80].…”